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 𝐴 ( 5 , 1 , 8 ) and 𝐵 ( 3 , 9 , 6 ) . Find the component of the vector V i j k = 5 2 + 2 in the direction 𝐴 𝐵 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 𝐴 = 5 , | | 𝐵 | | = 1 5 , and the measure of the angle between them is 3 0 , find the algebraic projection of 𝐵 in the direction of 𝐴 .

  • A 5 3 2
  • B 5 2
  • C 7 5 3 2
  • D 1 5 3 2
  • E 1 5 2

Q4:

Determine, to the nearest hundredth, the component of vector 𝑉 along 𝐴 𝐵 , given that 𝑉 = ( 7 , 2 , 1 0 ) and the coordinates of 𝐴 and 𝐵 are ( 1 , 4 , 8 ) and ( 3 , 2 , 0 ) , respectively.

Q5:

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

  • A 𝐵 𝜃 c o s
  • B 𝐴 𝐵 𝜃 c o s
  • C 𝐴 × 𝐵 𝜃 c o s
  • D 𝐴 𝜃 c o s
  • E 𝐴 × 𝐵 𝜃 c o s

Q6:

Determine the magnitude of the component of F i j = 2 3 + 1 7 in the direction of 𝐴 𝐵 , given that the coordinates of the points 𝐴 and 𝐵 are ( 2 , 3 ) and ( 6 , 6 ) respectively.

  • A0.2
  • B27.4
  • C8.2
  • D28.6

Q7:

Given that 𝐴 = ( 6 , 3 , 2 ) and 𝐵 = ( 4 , 1 , 6 ) , determine the component of 𝐴 along 𝐵 .

  • A 5 5 3 5 3
  • B 3 3 7
  • C 6 7
  • D 3 3 5 3 5 3

Q8:

Given that the measure of the smaller angle between 𝐴 and 𝐵 is 1 5 0 , and 𝐵 = 5 4 , determine the component of vector 𝐵 along 𝐴 .

  • A 1 8 3
  • B27
  • C54
  • D 2 7 3

Q9:

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

  • A22.4
  • B
  • C
  • D28

Q10:

𝐴 𝐵 𝐶 𝐷 is a trapezium, where 𝐴 𝐷 𝐵 𝐶 , 𝑚 𝐴 = 𝑚 𝐵 = 9 0 , 𝑚 𝐶 = 6 0 , 𝐴 𝐷 = 6 0 c m , and 𝐵 𝐶 = 1 0 1 c m . Determine the algebraic projection of 𝐶 𝐷 on the direction of 𝐶 𝐵 .

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 𝑂 𝐴 has length 10. Write this vector using 𝑖 , 𝑗 , and 𝑘 , with components accurate to two decimal places.

  • A 𝐴 = 1 . 2 8 𝑖 + 3 . 3 5 𝑗 + 9 . 3 4 𝑘
  • B 𝐴 = 3 . 5 8 𝑖 + 9 . 3 4 𝑗 + 9 . 3 4 𝑘
  • C 𝐴 = 8 . 7 2 𝑖 + 3 . 3 5 𝑗 + 3 . 5 8 𝑘
  • D 𝐴 = 3 . 3 5 𝑖 + 8 . 7 2 𝑗 + 3 . 5 8 𝑘

Q13:

Consider the points 𝐴 ( 7 , 6 , 0 ) and 𝐵 ( 5 , 7 , 4 ) . Find the component of the vector V i j k = 8 9 3 in the direction 𝐴 𝐵 rounded to the nearest hundredth.

Q14:

Consider the points 𝐴 ( 6 , 7 , 3 ) and 𝐵 ( 7 , 5 , 2 ) . Find the component of the vector V i j = 5 9 in the direction 𝐴 𝐵 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

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