# Worksheet: Vector Projection

In this worksheet, we will practice finding the projection of a vector onto another.

Q1:

The cube shown has sides of length . Find the scalar projection of onto , giving your answer correct to two decimal places. Q2:

is a right triangle at , where , , and is the midpoint of . Find the algebraic projection of in the direction of .

Q3:

Given that , , and the measure of the angle between and is , determine the algebraic projection of in the direction of .

Q4:

Determine, to the nearest hundredth, the length of the projection of the vector passing through the points and to the straight line .

Q5:

The cube shown has sides of length . Find the scalar projection of onto , giving your answer correct to two decimal places. Q6:

The cube shown has sides of length 30. Find the scalar projection of onto , giving your answer correct to two decimal places. Q7:

The cube shown has sides of length . Find the scalar projection of onto , giving your answer correct to two decimal places. Q8:

The cube shown has sides of length 25. Find the scalar projection of onto , giving your answer correct to two decimal places. Q9:

Consider the points and . Find the component of the vector in the direction rounded to the nearest hundredth.

Q10:

Given that is a square having a side length of 53 cm, calculate the algebraic projection of in the direction of .

Q11:

is a trapezoid, where , , , , and . Determine the algebraic projection of on the direction of .

Q12:

Determine whether the following is true or false: If the component of a vector in the direction of another vector is zero, then the two are perpendicular.

• Afalse
• Btrue

Q13:

is a right-angled triangle in which , and . Determine the algebraic projection of in the direction of , rounding your answer to two decimal places.

Q14:

Given that the measure of the smaller angle between and is , and , determine the component of vector along .

• A27
• B
• C54
• D

Q15:

If , , and the measure of the angle between them is , find the algebraic projection of in the direction of .

• A
• B
• C
• D
• E

Q16:

Determine, to the nearest hundredth, the component of vector along , given that and the coordinates of and are and , respectively.

Q17:

Find the component of vector in the direction of , where is the included angle between them.

• A
• B
• C
• D
• E

Q18:

Determine the magnitude of the component of in the direction of , given that the coordinates of the points and are and respectively.

Q19:

The vector has length 10. Write this vector using , , and , with components accurate to two decimal places. • A
• B
• C
• D

Q20:

Given that and , determine the component of along .

• A
• B
• C
• D

Q21:

Given that is a rectangle in which and , define the algebraic projection of in the direction of .

• A
• B75
• C65
• D10
• E