# Worksheet: The Angle between Two Vectors in the Coordinate Plane

In this worksheet, we will practice using the dot product to find the angle between two nonzero vectors in a plane.

Q1:

If and , where the measure of the angle between and is , find correct to the nearest hundredth.

Q2:

Suppose is a square of side 47. Determine .

Q3:

Suppose a rectangle with and . Determine .

Q4:

Find the value of approximated to the nearest hundredth. Q5:

. • A
• B
• C
• D
• E

Q6:

If and satisfy , how are the two vectors related?

• Aperpendicular
• Bparallel

Q7:

Consider a square of side 32.6. Determine .

Q8:

In a rectangle , and . Determine .

Q9:

If is a regular hexagon whose side is 7.1, find .

Q10:

If is a regular hexagon whose side is 9.6, find .

Q11:

Triangle has a right angle at . Given , , and that is the midpoint of . Determine to the nearest hundredth.

Q12:

Triangle has a right angle at . Given , , and that is the midpoint of , determine to the nearest hundredth.

Q13:

Triangle has a right angle at . Given and , determine .

Q14:

If and , find all the possible values of that make the measure of the angle between the two vectors .

• A or
• B or
• C or
• D or

Q15:

Let and Find the angle between and giving your answer to two decimal places.

Q16:

Given that , and , determine the angle between the two vectors rounded to the nearest minute.

• A
• B
• C
• D

Q17:

If , and is the angle between and , find the value of in the range .

Q18:

If , , and the measure of the angle between and is , calculate .

• A
• B
• C
• D80
• E

Q19:

If , find the value of in the range ,where is the angle between and .

Q20:

If is the angle between and and , find the value of in the range .

Q21:

Given that , , and the measure of the angle between and is , determine to the nearest hundredth.

Q22:

Between unit vectors and is an angle of . Find to the nearest tenth.

Q23:

If is the smaller angle between the two vectors and , find .

• A
• B
• C
• D
• E

Q24:

Given that , , and , determine the measure of the angle between and rounded to the nearest minute.

• A
• B
• C
• D

Q25:

Given that , , and , determine , and give the measure of the angle between and to the nearest hundredth.

• A,
• B,
• C,
• D,