Show All Notes Hide All Notes

Section 11.2 : 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