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)

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)
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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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