Question Solved1 Answer 12. A triangle is defined by the points \( A(0,1,2), B(1,0,2) \) and \( C(-1,2,0) \). Find angle \( A \) of this triangle. (4 marks)

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Transcribed Image Text: 12. A triangle is defined by the points \( A(0,1,2), B(1,0,2) \) and \( C(-1,2,0) \). Find angle \( A \) of this triangle. (4 marks)
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Transcribed Image Text: 12. A triangle is defined by the points \( A(0,1,2), B(1,0,2) \) and \( C(-1,2,0) \). Find angle \( A \) of this triangle. (4 marks)
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Step1/2.gkwtCW{margin:0;font-family:"Aspira Webfont","Helvetica","Arial",sans-serif;display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-flex-direction:column;-ms-flex-direction:column;flex-direction:column;gap:16px;}/*!sc*/data-styled.g366[id="sc-z3f5s1-0"]{content:"gkwtCW,"}/*!sc*/.iIwMoS{white-space:pre-wrap;}/*!sc*/data-styled.g368[id="sc-1aslxm9-0"]{content:"iIwMoS,"}/*!sc*/.fzJtOB{text-align:start;}/*!sc*/data-styled.g370[id="sc-1aslxm9-2"]{content:"fzJtOB,"}/*!sc*/.aczzN{line-height:1;font-size:80%;}/*!sc*/data-styled.g393[id="sc-1r1de4b-3"]{content:"aczzN,"}/*!sc*/.ePoHy{line-height:1;font-size:80%;}/*!sc*/data-styled.g394[id="sc-1r1de4b-4"]{content:"ePoHy,"}/*!sc*/.hOZehF{margin:0;font-family:"Aspira Webfont","Helvetica","Arial",sans-serif;}/*!sc*/data-styled.g397[id="sc-9wsboo-0"]{content:"hOZehF,"}/*!sc*/.evjWEY{padding:0 1.5px;}/*!sc*/data-styled.g398[id="sc-9wsboo-1"]{content:"evjWEY,"}/*!sc*/.lhIoTe{margin:0;font-size:1rem;}/*!sc*/data-styled.g399[id="sc-1swtczx-0"]{content:"lhIoTe,"}/*!sc*/.iHelzO{margin:0;font-family:"Aspira Webfont","Helvetica","Arial",sans-serif;line-height:normal;}/*!sc*/data-styled.g430[id="sc-1sugbjn-0"]{content:"iHelzO,"}/*!sc*/.kkKaFK{margin-top:14px;}/*!sc*/data-styled.g434[id="sc-1sugbjn-4"]{content:"kkKaFK,"}/*!sc*/.iQllJf{margin-top:14px;}/*!sc*/data-styled.g435[id="sc-1sugbjn-5"]{content:"iQllJf,"}/*!sc*/Given that a triangle is defined by the points A(0,1,2) , B(1,0,2) and C(-1,2,0)we have to find angle A of this triangleExplanation:Please refer to solution in this step.Step2/2mjx-container[jax="CHTML"]{line-height: 0;}mjx-container [space="2"]{margin-left: .167em;}mjx-container [space="3"]{margin-left: .222em;}mjx-container [size="s"]{font-size: 70.7%;}mjx-box{display: inline-block;}mjx-row{display: table-row;}mjx-row > *{display: table-cell;}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-mover{display: inline-block; text-align: left;}mjx-mover:not([limits="false"]){padding-top: .1em;}mjx-mover:not([limits="false"]) > *{display: block; text-align: left;}mjx-mo{display: inline-block; text-align: left;}mjx-stretchy-v{display: inline-block;}mjx-stretchy-v > *{display: block;}mjx-stretchy-v > * > mjx-c{transform: scaley(1.0000001); transform-origin: left center; overflow: hidden;}mjx-stretchy-v > mjx-ext{display: block; height: 100%; box-sizing: border-box; border: 0px solid transparent;overflow: hidden;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{display: inline-block;}mjx-mi{display: inline-block; text-align: left;}mjx-mrow{display: inline-block; text-align: left;}mjx-msqrt{display: inline-block; text-align: left;}mjx-surd{display: inline-block; vertical-align: top;}mjx-sqrt{display: inline-block; padding-top: .07em;}mjx-sqrt > mjx-box{border-top: .07em solid;}mjx-msup{display: inline-block; text-align: left;}mjx-mn{display: inline-block; text-align: left;}mjx-mfrac{display: inline-block; text-align: left;}mjx-frac{display: inline-block; vertical-align: 0.17em; padding: 0 .22em;}mjx-dtable{display: inline-table; width: 100%;}mjx-dtable > *{font-size: 2000%;}mjx-dbox{display: block; font-size: 5%;}mjx-num{display: block; text-align: center;}mjx-den{display: block; text-align: center;}mjx-nstrut{display: inline-block; height: .054em; width: 0; vertical-align: -.054em;}mjx-dstrut{display: inline-block; height: .505em; width: 0;}mjx-line{display: block; box-sizing: border-box; min-height: 1px; height: .06em; border-top: .06em solid; margin: .06em -.1em; overflow: hidden;}mjx-c::before{display: block; width: 0;}.MJX-TEX{font-family: MJXZERO, MJXTEX;}.TEX-I{font-family: MJXZERO, MJXTEX-I;}.TEX-S2{font-family: MJXZERO, MJXTEX-S2;}.TEX-V{font-family: MJXZERO, MJXTEX-V;}mjx-stretchy-v mjx-c{font-family: MJXZERO, MJXTEX-S1, MJXTEX-S4, MJXTEX, MJXTEX-A ! important;}@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-I; src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Math-Italic.woff") format("woff");}@font-face{font-family: MJXTEX-S1; src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Size1-Regular.woff") format("woff");}@font-face{font-family: MJXTEX-S2; src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Size2-Regular.woff") format("woff");}@font-face{font-family: MJXTEX-S4; src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Size4-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-stretchy-v.mjx-c7C mjx-ext mjx-c::before{content: "\2223"; width: 0.333em;}mjx-c.mjx-c20D7.TEX-V::before{padding: 0.714em 0.5em 0 0; content: "\2192";}mjx-c.mjx-c41::before{padding: 0.716em 0.75em 0 0; content: "A";}mjx-c.mjx-c42::before{padding: 0.683em 0.708em 0 0; content: "B";}mjx-c.mjx-c5E::before{padding: 0.694em 0.5em 0 0; content: "^";}mjx-c.mjx-c69::before{padding: 0.669em 0.278em 0 0; content: "i";}mjx-c.mjx-c6A::before{padding: 0.669em 0.306em 0.205em 0; content: "j";}mjx-c.mjx-c6B::before{padding: 0.694em 0.528em 0 0; content: "k";}mjx-c.mjx-c221A.TEX-S2::before{padding: 1.15em 1.02em 0.65em 0; content: "\221A";}mjx-c.mjx-c31::before{padding: 0.666em 0.5em 0 0; content: "1";}mjx-c.mjx-c32::before{padding: 0.666em 0.5em 0 0; content: "2";}mjx-c.mjx-c2B::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-c2212::before{padding: 0.583em 0.778em 0.082em 0; content: "\2212";}mjx-c.mjx-c29::before{padding: 0.75em 0.389em 0.25em 0; content: ")";}mjx-c.mjx-c30::before{padding: 0.666em 0.5em 0.022em 0; content: "0";}mjx-c.mjx-c221A::before{padding: 0.8em 0.853em 0.2em 0; content: "\221A";}mjx-c.mjx-c43::before{padding: 0.705em 0.722em 0.021em 0; content: "C";}mjx-c.mjx-c36::before{padding: 0.666em 0.5em 0.022em 0; content: "6";}mjx-c.mjx-c1D703.TEX-I::before{padding: 0.705em 0.469em 0.01em 0; content: "\3B8";}mjx-c.mjx-c63::before{padding: 0.448em 0.444em 0.011em 0; content: "c";}mjx-c.mjx-c6F::before{padding: 0.448em 0.5em 0.01em 0; content: "o";}mjx-c.mjx-c73::before{padding: 0.448em 0.394em 0.011em 0; content: "s";}mjx-c.mjx-c2061::before{padding: 0 0 0 0; content: "";}mjx-c.mjx-c2E::before{padding: 0.12em 0.278em 0 0; content: ".";}mjx-c.mjx-c33::before{padding: 0.665em 0.5em 0.022em 0; content: "3";}now AB→= (x2-x1)i^ + (y2-y1)j^ +(z2-z1)k^ = 1i^ -1j^ +0k^|AB→|= 12+(−1)2+0 = 2 AC→= (x3-x1)i^ + (y3-y1)j^ +(z3-z1)k^ = -1i^ +1j^ -2k^ |AC→|= (−1)2+(1)2+(−2)2 = 6Let θ is the angle A is the angle between the two angles AB→ and AC→Now cos⁡(θ)= AB→.AC→|AB→||AC→|= −1−1+012= -212= - 13θ = cos -1 ( - 13) 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 ! ... 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