# 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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**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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**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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**Q13: **

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

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**Q14: **

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

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- 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: **

The vector has length 10. Write this vector using , , and , with components accurate to two decimal places.

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