Lesson Worksheet: Scalar Projection Mathematics • 12th Grade

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

Q1:

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

  • A||×𝜃ABcos
  • B||𝜃Bcos
  • C||𝜃Acos
  • D||×𝜃ABcos
  • E(⋅)𝜃ABcos

Q2:

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

  • A67
  • B−337
  • C−33√5353
  • D−5√5353

Q3:

True or False: If the component of a vector in the direction of another vector is zero, then the two are perpendicular.

  • AFalse
  • BTrue

Q4:

Given that the measure of the smaller angle between A and B is 150∘, and ||=54B, determine the component of vector B along A.

  • A27
  • B−18√3
  • C54
  • D−27√3

Q5:

If ||=5A, ||=15B, and the measure of the angle between them is 30∘, find the algebraic projection of B in the direction of A.

  • A52
  • B152
  • C75√32
  • D15√32
  • E5√32

Q6:

Determine, to the nearest hundredth, the component of vector V along 𝐴𝐵, given that V=⟨−7,2,10⟩ and the coordinates of 𝐴 and 𝐵 are (1,−4,−8) and (3,2,0), respectively.

Q7:

𝐴𝐵𝐶 is a right triangle at 𝐵, where 𝐴𝐵=17cm, 𝐵𝐶=11cm, and 𝐷 is the midpoint of 𝐴𝐶. Find the algebraic projection of 𝐴𝐷 in the direction of 𝐶𝐵.

Q8:

Consider the points 𝐴(5,−1,−8) and 𝐵(−3,−9,−6). Find the component of the vector Vijk=−5−2+2 in the direction 𝐴𝐵 rounded to the nearest hundredth.

Q9:

If the scalar projection of vector A along vector B is 𝐴=1 and AB⋅=2, find ||B.

Q10:

The cube shown has sides of length 4417. Find the scalar projection of 𝑂𝐴 onto 𝐶𝐵, giving your answer correct to two decimal places.

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