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.

This lesson includes 16 additional questions and 190 additional question variations for subscribers.

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