Question Solved1 Answer hello, please all the questions below correclty and in a clear hand writing and all steps, and i promise you for thumbs up because i appricieate your work and your time 1. Let \( \vec{a}=(2,-2,3), \vec{b}=(1,3,4) \), and \( \vec{c}=(3,6,4) \). Find: a) \( \vec{a}+2 \vec{b}+3 \vec{c} \) (2) b) \( \vec{a} \cdot \vec{b} \) c) \( \vec{b} \times \vec{c} \) (2) d) \( |-3 \vec{a}+4 \vec{b}| \) (3) 2. Determine the magnitude of the vector components \( \left(\left|\vec{F}_{h}\right|\right. \) and \( \left|\overrightarrow{F_{v}}\right| \) ) of each of the following resultant vectors. a) \( 30 \mathrm{~N} \) at an inclination of \( 40^{\circ} \) counterclockwise from the horizontal. (2) Page 1 of 5 2. b) \( 50 \mathrm{~m} / \mathrm{s}, 50^{\prime \prime} \) clockw/se from the horizontal. (2) c) \( 1200 \mathrm{~N}, 70^{\prime \prime} \) clockwise from the vertical. (2) Thinking/Inquiry (13 marks) 7. Let \( \vec{a}=(2,-2,3), \vec{b}=(1,3,4) \), and \( \vec{c}=(3,6,4) \). Find: (6 marks) a) \( (\vec{a} \times \vec{b}) \times \vec{c} \) b) \( (\vec{a} \times \vec{b}) \cdot \vec{c} \) 8. Consider the vectors \( \vec{u}=(2,-1,1) \) and \( \vec{v}=(1,1,2) \). Determine the angle \( \theta \) between \( \vec{u} \) and \( \vec{v} \). (3 marks) 9. Show that the vector \( \vec{a}=(5,9,14) \) can be written as a linear combination of the vectors \( \vec{b} \) and \( \vec{c} \), where \( \vec{b}=(-2,3,1) \) and \( \vec{c}=(3,1,4) \) (4 marks)

EXKDYS The Asker · Calculus

hello, please all the questions below correclty and in a clear hand writing and all steps, and i promise you for thumbs up because i appricieate your work and your time

Transcribed Image Text: 1. Let \( \vec{a}=(2,-2,3), \vec{b}=(1,3,4) \), and \( \vec{c}=(3,6,4) \). Find: a) \( \vec{a}+2 \vec{b}+3 \vec{c} \) (2) b) \( \vec{a} \cdot \vec{b} \) c) \( \vec{b} \times \vec{c} \) (2) d) \( |-3 \vec{a}+4 \vec{b}| \) (3) 2. Determine the magnitude of the vector components \( \left(\left|\vec{F}_{h}\right|\right. \) and \( \left|\overrightarrow{F_{v}}\right| \) ) of each of the following resultant vectors. a) \( 30 \mathrm{~N} \) at an inclination of \( 40^{\circ} \) counterclockwise from the horizontal. (2) Page 1 of 5 2. b) \( 50 \mathrm{~m} / \mathrm{s}, 50^{\prime \prime} \) clockw/se from the horizontal. (2) c) \( 1200 \mathrm{~N}, 70^{\prime \prime} \) clockwise from the vertical. (2) Thinking/Inquiry (13 marks) 7. Let \( \vec{a}=(2,-2,3), \vec{b}=(1,3,4) \), and \( \vec{c}=(3,6,4) \). Find: (6 marks) a) \( (\vec{a} \times \vec{b}) \times \vec{c} \) b) \( (\vec{a} \times \vec{b}) \cdot \vec{c} \) 8. Consider the vectors \( \vec{u}=(2,-1,1) \) and \( \vec{v}=(1,1,2) \). Determine the angle \( \theta \) between \( \vec{u} \) and \( \vec{v} \). (3 marks) 9. Show that the vector \( \vec{a}=(5,9,14) \) can be written as a linear combination of the vectors \( \vec{b} \) and \( \vec{c} \), where \( \vec{b}=(-2,3,1) \) and \( \vec{c}=(3,1,4) \) (4 marks)
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Transcribed Image Text: 1. Let \( \vec{a}=(2,-2,3), \vec{b}=(1,3,4) \), and \( \vec{c}=(3,6,4) \). Find: a) \( \vec{a}+2 \vec{b}+3 \vec{c} \) (2) b) \( \vec{a} \cdot \vec{b} \) c) \( \vec{b} \times \vec{c} \) (2) d) \( |-3 \vec{a}+4 \vec{b}| \) (3) 2. Determine the magnitude of the vector components \( \left(\left|\vec{F}_{h}\right|\right. \) and \( \left|\overrightarrow{F_{v}}\right| \) ) of each of the following resultant vectors. a) \( 30 \mathrm{~N} \) at an inclination of \( 40^{\circ} \) counterclockwise from the horizontal. (2) Page 1 of 5 2. b) \( 50 \mathrm{~m} / \mathrm{s}, 50^{\prime \prime} \) clockw/se from the horizontal. (2) c) \( 1200 \mathrm{~N}, 70^{\prime \prime} \) clockwise from the vertical. (2) Thinking/Inquiry (13 marks) 7. Let \( \vec{a}=(2,-2,3), \vec{b}=(1,3,4) \), and \( \vec{c}=(3,6,4) \). Find: (6 marks) a) \( (\vec{a} \times \vec{b}) \times \vec{c} \) b) \( (\vec{a} \times \vec{b}) \cdot \vec{c} \) 8. Consider the vectors \( \vec{u}=(2,-1,1) \) and \( \vec{v}=(1,1,2) \). Determine the angle \( \theta \) between \( \vec{u} \) and \( \vec{v} \). (3 marks) 9. Show that the vector \( \vec{a}=(5,9,14) \) can be written as a linear combination of the vectors \( \vec{b} \) and \( \vec{c} \), where \( \vec{b}=(-2,3,1) \) and \( \vec{c}=(3,1,4) \) (4 marks)
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Step1/4mjx-container[jax="CHTML"]{line-height: 0;}mjx-container [space="2"]{margin-left: .167em;}mjx-container [space="3"]{margin-left: .222em;}mjx-container [space="4"]{margin-left: .278em;}mjx-itable{display: inline-table;}mjx-mtext{display: inline-block; text-align: left;}mjx-assistive-mml{position: absolute !important; top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); padding: 1px 0px 0px 0px !important; border: 0px !important; display: block !important; width: auto !important; overflow: hidden !important; -webkit-touch-callout: none; -webkit-user-select: none; -khtml-user-select: none; -moz-user-select: none; -ms-user-select: none; user-select: none;}mjx-math{display: inline-block; text-align: left; line-height: 0; text-indent: 0; font-style: normal; font-weight: normal; font-size: 100%; font-size-adjust: none; letter-spacing: normal; border-collapse: collapse; word-wrap: normal; word-spacing: normal; white-space: nowrap; direction: ltr; padding: 1px 0;}mjx-mtable{display: inline-block; 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text-align: left;}mjx-mn{display: inline-block; text-align: left;}mjx-c::before{display: block; width: 0;}.MJX-TEX{font-family: MJXZERO, MJXTEX;}.TEX-A{font-family: MJXZERO, MJXTEX-A;}.TEX-V{font-family: MJXZERO, MJXTEX-V;}@font-face{font-family: MJXZERO; src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Zero.woff") format("woff");}@font-face{font-family: MJXTEX; src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Main-Regular.woff") format("woff");}@font-face{font-family: MJXTEX-A; src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_AMS-Regular.woff") format("woff");}@font-face{font-family: MJXTEX-V; src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Vector-Regular.woff") format("woff");}mjx-c.mjx-c20D7.TEX-V::before{padding: 0.714em 0.5em 0 0; content: "\2192";}mjx-c.mjx-c61::before{padding: 0.448em 0.5em 0.011em 0; content: "a";}mjx-c.mjx-c3D::before{padding: 0.583em 0.778em 0.082em 0; content: "=";}mjx-c.mjx-c28::before{padding: 0.75em 0.389em 0.25em 0; content: "(";}mjx-c.mjx-c32::before{padding: 0.666em 0.5em 0 0; content: "2";}mjx-c.mjx-c2C::before{padding: 0.121em 0.278em 0.194em 0; content: ",";}mjx-c.mjx-c2212::before{padding: 0.583em 0.778em 0.082em 0; content: "\2212";}mjx-c.mjx-c33::before{padding: 0.665em 0.5em 0.022em 0; content: "3";}mjx-c.mjx-c29::before{padding: 0.75em 0.389em 0.25em 0; content: ")";}mjx-c.mjx-c62::before{padding: 0.694em 0.556em 0.011em 0; content: "b";}mjx-c.mjx-c31::before{padding: 0.666em 0.5em 0 0; content: "1";}mjx-c.mjx-c34::before{padding: 0.677em 0.5em 0 0; content: "4";}mjx-c.mjx-c63::before{padding: 0.448em 0.444em 0.011em 0; content: "c";}mjx-c.mjx-c36::before{padding: 0.666em 0.5em 0.022em 0; content: "6";}mjx-c.mjx-cA0::before{padding: 0 0.25em 0 0; content: "\A0";}mjx-c.mjx-c2234.TEX-A::before{padding: 0.471em 0.667em 0.082em 0; content: "\2234";}mjx-c.mjx-c2B::before{padding: 0.583em 0.778em 0.082em 0; content: "+";}mjx-c.mjx-c38::before{padding: 0.666em 0.5em 0.022em 0; content: "8";}mjx-c.mjx-c39::before{padding: 0.666em 0.5em 0.022em 0; content: "9";}Here the given vectors are a→=(2,−2,3),b→=(1,3,4),c→=(3,6,4) ∴a→+2b→+3c→ =(2,−2,3)+2(1,3,4)+3(3,6,4) =(2,−2,3)+(2,6,8)+(9,18,12) =(2+2+9,−2+6+18,3+8+12) =(13,22,23) Explanation:mjx-container[jax="CHTML"] { line-height: 0;}mjx-container [space="1"] { margin-left: .111em;}mjx-container [space="2"] { margin-left: .167em;}mjx-container [space="3"] { margin-left: .222em;}mjx-container [space="4"] { margin-left: .278em;}mjx-container [space="5"] { margin-left: .333em;}mjx-container [rspace="1"] { margin-right: .111em;}mjx-container [rspace="2"] { margin-right: .167em;}mjx-container [rspace="3"] { margin-right: .222em;}mjx-container [rspace="4"] { margin-right: .278em;}mjx-container [rspace="5"] { margin-right: .333em;}mjx-container [size="s"] { font-size: 70.7%;}mjx-container [size="ss"] { font-size: 50%;}mjx-container [size="Tn"] { font-size: 60%;}mjx-container [size="sm"] { font-size: 85%;}mjx-container [size="lg"] { font-size: 120%;}mjx-container [size="Lg"] { font-size: 144%;}mjx-container [size="LG"] { font-size: 173%;}mjx-container [size="hg"] { font-size: 207%;}mjx-container [size="HG"] { font-size: 249%;}mjx-container [width="full"] { width: 100%;}mjx-box { display: inline-block;}mjx-block { display: block;}mjx-itable { display: inline-table;}mjx-row { display: table-row;}mjx-row > * { display: table-cell;}mjx-mtext { display: inline-block;}mjx-mstyle { display: inline-block;}mjx-merror { display: inline-block; color: red; background-color: yellow;}mjx-mphantom { visibility: hidden;}_::-webkit-full-page-media, _:future, :root mjx-container { will-change: opacity;}mjx-assistive-mml { position: absolute !important; top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); padding: 1px 0px 0px 0px !important; border: 0px !important; display: block !important; width: auto !important; overflow: hidden !important; -webkit-touch-callout: none; -webkit-user-select: none; -khtml-user-select: none; -moz-user-select: none; -ms-user-select: none; user-select: none;}mjx-assistive-mml[display="block"] { width: 100% !important;}mjx-math { display: inline-block; text-align: left; line-height: 0; text-indent: 0; font-style: normal; font-weight: normal; font-size: 100%; font-size-adjust: none; letter-spacing: normal; border-collapse: collapse; word-wrap: normal; word-spacing: normal; white-space: nowrap; direction: ltr; padding: 1px 0;}mjx-container[jax="CHTML"][display="true"] { display: block; text-align: center; 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transform-origin: left center; overflow: hidden;}mjx-stretchy-v > mjx-ext { display: block; height: 100%; box-sizing: border-box; border: 0px solid transparent; /* IE */ overflow: hidden; /* others */ overflow: visible clip;}mjx-stretchy-v > mjx-ext > mjx-c::before { width: initial; box-sizing: border-box;}mjx-stretchy-v > mjx-ext > mjx-c { transform: scaleY(500) translateY(.075em); overflow: visible;}mjx-mark { display: inline-block; height: 0px;}mjx-c::before { display: block; width: 0;}.MJX-TEX { font-family: MJXZERO, MJXTEX;}.TEX-B { font-family: MJXZERO, MJXTEX-B;}.TEX-I { font-family: MJXZERO, MJXTEX-I;}.TEX-MI { font-family: MJXZERO, MJXTEX-MI;}.TEX-BI { font-family: MJXZERO, MJXTEX-BI;}.TEX-S1 { font-family: MJXZERO, MJXTEX-S1;}.TEX-S2 { font-family: MJXZERO, MJXTEX-S2;}.TEX-S3 { font-family: MJXZERO, MJXTEX-S3;}.TEX-S4 { font-family: MJXZERO, MJXTEX-S4;}.TEX-A { font-family: MJXZERO, MJXTEX-A;}.TEX-C { font-family: MJXZERO, MJXTEX-C;}.TEX-CB { font-family: MJXZERO, MJXTEX-CB;}.TEX-FR { font-family: MJXZERO, MJXTEX-FR;}.TEX-FRB { font-family: MJXZERO, MJXTEX-FRB;}.TEX-SS { font-family: MJXZERO, MJXTEX-SS;}.TEX-SSB { font-family: MJXZERO, MJXTEX-SSB;}.TEX-SSI { font-family: MJXZERO, MJXTEX-SSI;}.TEX-SC { font-family: MJXZERO, MJXTEX-SC;}.TEX-T { font-family: MJXZERO, MJXTEX-T;}.TEX-V { font-family: MJXZERO, MJXTEX-V;}.TEX-VB { font-family: MJXZERO, MJXTEX-VB;}mjx-stretchy-v mjx-c, mjx-stretchy-h mjx-c { font-family: MJXZERO, MJXTEX-S1, MJXTEX-S4, MJXTEX, MJXTEX-A ! important;}@font-face /* 0 */ { font-family: MJXZERO; 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src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Typewriter-Regular.woff") format("woff");}@font-face /* 20 */ { font-family: MJXTEX-V; src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Vector-Regular.woff") format("woff");}@font-face /* 21 */ { font-family: MJXTEX-VB; src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Vector-Bold.woff") format("woff");}mjx-c.mjx-c63::before { padding: 0.448em 0.444em 0.011em 0; content: "c";}mjx-c.mjx-c28::before { padding: 0.75em 0.389em 0.25em 0; content: "(";}mjx-c.mjx-c78::before { padding: 0.431em 0.528em 0 0; content: "x";}mjx-c.mjx-c2C::before { padding: 0.121em 0.278em 0.194em 0; content: ",";}mjx-c.mjx-c79::before { padding: 0.431em 0.528em 0.204em 0; content: "y";}mjx-c.mjx-c7A::before { padding: 0.431em 0.444em 0 0; content: "z";}mjx-c.mjx-c29::before { padding: 0.75em 0.389em 0.25em 0; content: ")";}mjx-c.mjx-c3D::before { padding: 0.583em 0.778em 0.082em 0; content: "=";}Here we have used the formula c(x,y,z)=(cx,cy,cz) where c is a scalar .Step2/4mjx-container[jax="CHTML"]{line-height: 0;}mjx-container [space="2"]{margin-left: .167em;}mjx-container [space="3"]{margin-left: .222em;}mjx-container [space="4"]{margin-left: .278em;}mjx-itable{display: inline-table;}mjx-assistive-mml{position: absolute !important; top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); padding: 1px 0px 0px 0px !important; border: 0px !important; display: block !important; width: auto !important; overflow: hidden !important; -webkit-touch-callout: none; -webkit-user-select: none; -khtml-user-select: none; -moz-user-select: none; -ms-user-select: none; user-select: none;}mjx-math{display: inline-block; text-align: left; line-height: 0; text-indent: 0; font-style: normal; font-weight: normal; font-size: 100%; font-size-adjust: none; letter-spacing: normal; border-collapse: collapse; word-wrap: normal; word-spacing: normal; white-space: nowrap; direction: ltr; padding: 1px 0;}mjx-mtable{display: inline-block; text-align: center; vertical-align: .25em; position: relative; box-sizing: border-box; border-spacing: 0; border-collapse: collapse;}mjx-table{display: inline-block; vertical-align: -.5ex; box-sizing: border-box;}mjx-table > mjx-itable{vertical-align: middle; text-align: left; box-sizing: border-box;}mjx-mtr{display: table-row; text-align: left;}mjx-mtd{display: table-cell; text-align: center; padding: .215em .4em;}mjx-mtd:first-child{padding-left: 0;}mjx-mtd:last-child{padding-right: 0;}mj ... 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