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If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
Section 11.2 : Vector Arithmetic
- Given \(\vec a = 3\vec i - 9\vec j\) and \(\vec b = - 6\vec i + \vec j\) compute each of the following.
- \(10\vec b\)
- \(14\vec a + 20\vec b\)
- \(\left\| {8\vec b - \frac{1}{3}\vec a} \right\|\)
- Given \(\vec u = \left\langle {0,4, - 1} \right\rangle \) and \(\vec v = \left\langle {6, - 2, - 7} \right\rangle \) compute each of the following.
- \(\frac{3}{4}\vec u\)
- \( - 3\vec u - 7\vec v\)
- \(\left\| {\vec v + 10\vec u} \right\|\)
- Given \(\vec p = \left\langle {3, - 1, - 2} \right\rangle \) and \(\vec q = - \frac{1}{3}\vec i - \frac{1}{2}\vec k\) compute each of the following.
- \(2\vec p\)
- \(9\vec q - 2\vec p\)
- \(\left\| {8\vec p - 12\vec q} \right\|\)
- Find a unit vector that points in the same direction as \(\vec a = \left\langle {10, - 3,8, - 2} \right\rangle \).
- Find a unit vector that points in the same direction as \(\vec w = - \vec i - 6\vec j\).
- Find a unit vector that points in the opposite direction as \(\vec c = 2\vec i + 7\vec j - 5\vec k\).
- Find a unit vector that points in the opposite direction as \(\vec b = \left\langle {0, - 3, - 11} \right\rangle \).
- Find a vector that points in the same direction as \(\vec p = 2\vec i - 3\vec j + \vec k\) with a magnitude of \(\frac{1}{2}\).
- Find a vector that points in the opposite direction as \(\vec a = \left\langle { - 3, - 14,2} \right\rangle \) with a magnitude of 32.
- Find a vector that points in the same direction as \(\vec b = - 3\vec i + 2\vec k\) with a magnitude that is \(\frac{1}{{10}}\) the magnitude of \(\vec b\).
- Determine if \(\vec p = 8\vec i - 3\vec j\) and \(\vec q = 16\vec i - 6\vec j\) are parallel vectors.
- Determine if \(\vec v = \left\langle {1,0, - 4} \right\rangle \) and \(\vec w = \left\langle {9,3,1} \right\rangle \) are parallel vectors.
- Determine if \(\vec a = 10\vec i + 8\vec j + 20\vec k\) and \(b = \left\langle { - 35, - 28,70} \right\rangle \) are parallel vectors.
- Prove the property : \(\vec u + \left( {\vec v + \vec w} \right) = \left( {\vec u + \vec v} \right) + \vec w\).
- Prove the property : \(\vec v + \vec 0 = \vec v\).
- Prove the property : \(1\vec v = \vec v\).
- Prove the property : \(\left( {a + b} \right)\vec v = a\vec v + b\vec v\).