# 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.

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**Q2: **

Find the vector of norm 61 and direction cosines .

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**Q3: **

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

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**Q4: **

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

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**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.

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**Q6: **

Find the direction angles of the vector .

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**Q7: **

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

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**Q8: **

Find the direction cosines of the vector .

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**Q9: **

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

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**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.

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**Q12: **

Find the vector of norm 59 and direction cosines .

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- E

**Q13: **

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

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- C

**Q14: **

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

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**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 .

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