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May 6, 2021

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### Section 5-2 : Vector Arithmetic

1. Given $$\vec a = \left\langle {8,5} \right\rangle$$ and $$\vec b = \left\langle { - 3,6} \right\rangle$$ compute each of the following.
1. $$6\vec a$$
2. $$7\vec b - 2\vec a$$
3. $$\left\| {10\vec a + 3\vec b} \right\|$$
Solution
2. Given $$\vec u = 8\vec i - \vec j + 3\vec k$$ and $$\vec v = 7\vec j - 4\vec k$$ compute each of the following.
1. $$- 3\vec v$$
2. $$12\vec u + \vec v$$
3. $$\left\| { - 9\vec v - 2\vec u} \right\|$$
Solution
3. Find a unit vector that points in the same direction as $$\vec q = \vec i + 3\vec j + 9\vec k$$. Solution
4. Find a vector that points in the same direction as $$\vec c = \left\langle { - 1,4} \right\rangle$$ with a magnitude of 10. Solution
5. Determine if $$\vec a = \left\langle {3, - 5,1} \right\rangle$$ and $$\vec b = \left\langle {6, - 2,2} \right\rangle$$ are parallel vectors. Solution
6. Determine if $$\vec v = 9\vec i - 6\vec j - 24\vec k$$ and $$\vec w = \left\langle { - 15,10,40} \right\rangle$$ are parallel vectors. Solution
7. Prove the property : $$\vec v + \vec w = \vec w + \vec v$$. Solution