Worksheet: Vector Projection

In this worksheet, we will practice finding the component of a vector in the direction of another vector.

Q1:

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

Q2:

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

Q3:

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

• A
• B
• C
• D
• E

Q4:

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

Q5:

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

• A
• B
• C
• D
• E

Q6:

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

Q7:

Given that and , determine the component of along .

• A
• B
• C
• D

Q8:

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

• A
• B27
• C54
• D

Q9:

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

• A22.4
• B
• C
• D28

Q10:

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

Q11:

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

Q12:

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

• A
• B
• C
• D

Q13:

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

Q14:

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

Q15:

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

• A3.76
• B
• C
• D8