Lesson Worksheet: Cross Product in 2D Mathematics

In this worksheet, we will practice finding the cross product of two vectors in the coordinate plane.


All the sides of rhombus 𝑂𝐡𝐢𝐴 are of length 5. Suppose that sinβˆ π΄π‘‚π΅=34 and that 𝐴𝐡>𝑂𝐢. Use vector multiplication to find the lengths of the two diagonals.

  • A𝑂𝐢=1.84, 𝐴𝐡=4.08
  • B𝑂𝐢=4.11, 𝐴𝐡=9.11
  • C𝑂𝐢=16.93, 𝐴𝐡=26.54
  • D𝑂𝐢=4.11, 𝐴𝐡=3.27


Given that A=βŸ¨βˆ’2,7⟩ and B=⟨3,βˆ’8⟩, determine the area of the parallelogram whose adjacent sides are represented by A and B.


If |Γ—|+|β‹…|=17,424ABAB and ||=12A, find ||B.


𝐴𝐡𝐢𝐷 is a square of side 4, and u is a unit vector perpendicular to the square’s plane. Find οƒ π΄π·Γ—οƒŸπ΅πΆ.


In the rectangle 𝐴𝐡𝐢𝐷 shown in the figure, calculate 𝐷𝐴×𝐡𝑀 if {,,}ijk form a right-hand system of unit vectors.

  • A32k
  • B64k
  • Cβˆ’32k
  • Dβˆ’64k


If A=βŸ¨βˆ’7,3⟩, B=βŸ¨βˆ’7,7⟩, ACβŠ™=βˆ’75, and CBkΓ—=35, find C.

  • A⟨9,βˆ’4⟩
  • B⟨1,βˆ’4⟩
  • C⟨9,βˆ’11⟩
  • DβŸ¨βˆ’1,βˆ’4⟩


Given that Aij=7+2, Bij=βˆ’+2, and Cij=6+6, determine (+)Γ—CAB.

  • A30k
  • B34k
  • Cβˆ’30k
  • D3k


If Aij=βˆ’βˆ’2, Bij=βˆ’4βˆ’4, ACkΓ—=βˆ’3, and CBkΓ—=4, find C.

  • Aij+5
  • Bβˆ’2βˆ’ij
  • Cijβˆ’
  • Dβˆ’5βˆ’ij


If Aij=3βˆ’5, Bij=π‘š+5, and ABkΓ—=50, find the value of π‘š.


Given that 𝐴𝐡𝐢𝐷 is a square with side length 27 cm, and e is the unit vector perpendicular to its plane, determine 𝐴𝐡×𝐢𝐴.

  • A27e
  • B54e
  • C13e
  • D729e

This lesson includes 18 additional questions and 179 additional question variations for subscribers.

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