Lesson Worksheet: Scalar Projection Mathematics • 12th Grade

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


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


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

  • A67
  • B337
  • C335353
  • D55353


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

  • AFalse
  • BTrue


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
  • B183
  • C54
  • D273


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
  • C7532
  • D1532
  • E532


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.


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.


Consider the points 𝐴(5,1,8) and 𝐵(3,9,6). Find the component of the vector Vijk=52+2 in the direction 𝐴𝐵 rounded to the nearest hundredth.


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


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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