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Worksheet: Vector Projection

Q1:

Consider the points 𝐴 ( 5 , βˆ’ 1 , βˆ’ 8 ) and 𝐡 ( βˆ’ 3 , βˆ’ 9 , βˆ’ 6 ) . Find the component of the vector V i j k = βˆ’ 5 βˆ’ 2 + 2 in the direction  𝐴 𝐡 rounded to the nearest hundredth.

Q2:

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

Q3:

Consider the points 𝐴 ( βˆ’ 6 , 7 , 3 ) and 𝐡 ( βˆ’ 7 , βˆ’ 5 , βˆ’ 2 ) . Find the component of the vector V i j = 5 βˆ’ 9 in the direction  𝐴 𝐡 rounded to the nearest hundredth.

Q4:

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

Q5:

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

  • A20.5
  • B
  • C35.51
  • D41
  • E30

Q6:

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

Q7:

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

  • A22.4
  • B
  • C
  • D28

Q8:

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

  • A3.76
  • B
  • C
  • D8

Q9:

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

  • A
  • B27
  • C54
  • D

Q10:

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

  • A
  • B
  • C
  • D
  • E

Q11:

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

Q12:

Determine, to the nearest hundredth, the component of vector V along οƒ  𝐴 𝐡 , given that V = ⟨ 5 , 7 , βˆ’ 9 ⟩ and the coordinates of 𝐴 and 𝐡 are ( βˆ’ 1 , βˆ’ 3 , βˆ’ 5 ) and ( βˆ’ 3 , βˆ’ 1 0 , βˆ’ 9 ) , respectively.

Q13:

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

  • A
  • B
  • C
  • D
  • E

Q14:

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

Q15:

Given that A = ⟨ βˆ’ 6 , 3 , βˆ’ 2 ⟩ and B = ⟨ 4 , 1 , 6 ⟩ , determine the component of A along B .

  • A βˆ’ 5 √ 5 3 5 3
  • B βˆ’ 3 3 7
  • C 6 7
  • D βˆ’ 3 3 √ 5 3 5 3