Calculus Review Sheet #1



Name: ______________

Date: _______________

Pre-Calculus Review Sheet #25

Definitions

Vector

Magnitude

Orthogonal Vector

Parallel Vector

Formula

Angle Between Two Vectors

Projection of u onto v

Dot product

Unit Vector

Problems (Show all steps and round to the nearest hundredth.)

1. Find the component form of the vector v with Initial Point: (1,5) and Terminal Point: (15,9).

2. Find a unit vector in the direction of PQ if P(0,3) and Q(5,-8)

3. Are the following vectors orthogonal, parallel, or neither. [pic]?

4. Find the angle between u and v: [pic]

5. Find the projvu: [pic]

6. Find the trigonometric form of the complex number: [pic]

7. Write the complex number in standard form: [pic].

8. Use DeMoivre’s Theorem to find the indicated power of the complex number expressed in standard form: [pic]

9. Find the fourth roots of 256.

10. Let [pic] and [pic]. Find 3u; u + v; v – u; and 2u – 7v

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