# 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)

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)