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May 6, 2021

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### Section 5-1 : Basic Concepts

1. Describe the difference between $$\left( {4, - 1} \right)$$ and $$\left\langle {4, - 1} \right\rangle$$. Illustrate the difference with a sketch.

For problems 2 – 6 give the vector for the set of points. Find its magnitude and determine if the vector is a unit vector.

1. The line segment from $$\left( {6, - 2,3} \right)$$ to $$\left( { - 3, - 2,1} \right)$$.
2. The line segment from $$\displaystyle \left( {1, - \frac{1}{5}} \right)$$ to $$\displaystyle \left( {\frac{8}{5},\frac{3}{5}} \right)$$.
3. The line segment from $$\left( {2, - 1,5} \right)$$ to $$\left( {8, - 3, - 6} \right)$$.
4. The position vector for $$\left( { - 12,4,8} \right)$$.
5. The position vector for $$\left( {\cos \left( \theta \right),\sin \left( \theta \right)} \right)$$ for any angle $$\theta$$.
6. The vector $$\vec v = \left\langle { - 8, - 3} \right\rangle$$ starts at the point $$P = \left( {8,2} \right)$$. At what point does the vector end?
7. The vector $$\vec v = \left\langle {0,5, - 3} \right\rangle$$ starts at the point $$P = \left( { - 1,0,5} \right)$$. At what point does the vector end?
8. The vector $$\vec v = \left\langle { - 8, - 3} \right\rangle$$ ends at the point $$P = \left( {8,2} \right)$$. At what point does the vector start?
9. The vector $$\vec v = \left\langle {4, - 2,1} \right\rangle$$ ends at the point $$P = \left( {7, - 7,2} \right)$$. At what point does the vector start?