# Worksheet: Direction Angles and Direction Cosines

In this worksheet, we will practice finding direction angles and direction cosines for a given vector in space.

**Q1: **

Find the direction cosines of the vector that lies in the positive coordinate plane and makes an angle of with the positive -axis.

- A
- B
- C
- D
- E

**Q2: **

Find the vector of norm 61 and direction cosines .

- A
- B
- C
- D
- E

**Q3: **

The direction angles of are , , and . Which of the following planes contains ?

- A
- B
- C

**Q4: **

Find vector whose norm is 41 and whose direction angles are .

- A
- B
- C
- D

**Q5: **

Find the algebraic form of a vector if its norm is 31, given that it makes equal angles with the positive directions of the Cartesian axes.

- A
- B
- C

**Q6: **

Find the direction angles of the vector .

- A
- B
- C
- D
- E

**Q7: **

If , find the measure of the angle that makes with the positive direction of the -axis approximated to the nearest second.

- A
- B
- C
- D

**Q8: **

Find the direction cosines of the vector .

- A
- B
- C
- D

**Q9: **

Suppose that , and are the direction angles of a vector. Which of the following, to the nearest hundredth, is ?

- A
- B
- C
- D

**Q10: **

Find the measure of the direction angles of the vector , represented by the given figure, corrected to one decimal place.

- A, ,
- B, ,
- C, ,
- D, ,

**Q11: **

Find, to the nearest second, the measure of the angle that vector makes with the -axis.

- A
- B
- C

**Q12: **

Find the vector of norm 59 and direction cosines .

- A
- B
- C
- D
- E

**Q13: **

The direction angles of are , , and . Which of the following planes contains ?

- A
- B
- C

**Q14: **

The direction angles of are , , and . Which of the following planes contains ?

- A
- B
- C

**Q15: **

The given figure represents a vector whose norm is 5 units. Find the measure of the direction angles of rounded to one decimal place.

- A, ,
- B, ,
- C, ,
- D, ,

**Q16: **

Suppose that and has direction cosines , , and . Determine , where .

- A
- B
- C
- D