Lesson Worksheet: Cross Product in 2D Mathematics

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

Q1:

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

Q2:

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.

Q3:

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

Q4:

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.

Q5:

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

Q6:

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⟩

Q7:

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

  • A30k
  • B34k
  • Cβˆ’30k
  • D3k

Q8:

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

Q9:

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

Q10:

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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