# Question Solved1 Answerhello, 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)

O9Z046 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)
More
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)
See Answer
Add Answer +20 Points
Community Answer
OU47SY
See all the answers with 1 Unlock
Get 4 Free Unlocks by registration

Step1/1.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.g367[id="sc-z3f5s1-0"]{content:"gkwtCW,"}/*!sc*/.iIwMoS{white-space:pre-wrap;}/*!sc*/data-styled.g369[id="sc-1aslxm9-0"]{content:"iIwMoS,"}/*!sc*/.fzJtOB{text-align:start;}/*!sc*/data-styled.g371[id="sc-1aslxm9-2"]{content:"fzJtOB,"}/*!sc*/.hOZehF{margin:0;font-family:"Aspira Webfont","Helvetica","Arial",sans-serif;}/*!sc*/data-styled.g398[id="sc-9wsboo-0"]{content:"hOZehF,"}/*!sc*/.lhIoTe{margin:0;font-size:1rem;}/*!sc*/data-styled.g400[id="sc-1swtczx-0"]{content:"lhIoTe,"}/*!sc*/.dmyQem{margin:0;font-family:"Aspira Webfont","Helvetica","Arial",sans-serif;font-size:0.75rem;width:100%;text-align:center;}/*!sc*/data-styled.g426[id="sc-1uwiggj-0"]{content:"dmyQem,"}/*!sc*/.fwnwKl{max-width:70%;}/*!sc*/data-styled.g427[id="sc-1uwiggj-1"]{content:"fwnwKl,"}/*!sc*/.iHelzO{margin:0;font-family:"Aspira Webfont","Helvetica","Arial",sans-serif;line-height:normal;}/*!sc*/data-styled.g433[id="sc-1sugbjn-0"]{content:"iHelzO,"}/*!sc*/.kkKaFK{margin-top:14px;}/*!sc*/data-styled.g437[id="sc-1sugbjn-4"]{content:"kkKaFK,"}/*!sc*/.iQllJf{margin-top:14px;}/*!sc*/data-styled.g438[id="sc-1sugbjn-5"]{content:"iQllJf,"}/*!sc*/Given that vectors a,b and c:Q1 Solution: Given that@{:[ vec(c)=(3","6","4)],[ vec(a)+2 vec(b)+3 vec(c)=(2","-2","3)+2(1","3","4)],[+3(3","6","4)],[=(2","-2","3)+(2","6","8)+(9","18","12)],[=(13","22","23)]:}(b){:[ vec(a)* vec(b)=(2","-2","3)*(1","3","4)],[=2(1)-2(3)+3(4)],[=2-6+12],[=8]:}(c){:[ vec(b)xx vec(c)=|[ hat(ı), hat(ȷ), hat(k)],[1,3,4],[3,6,4]|],[=(12-24) hat(ı)-(4- ... See the full answer