# 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-angled 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 trapezium, 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.

- Atrue
- Bfalse

**Q13: **

is a right-angled triangle in which , and . Determine the algebraic projection of in the direction of .

- A22.4
- B
- C
- D28

**Q14: **

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

- A
- B27
- 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.

- A0.2
- B27.4
- C8.2
- D28.6

**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