# 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