Lesson Worksheet: Dot Product in 2D Mathematics • 12th Grade

In this worksheet, we will practice finding the dot product of two vectors in 2D.


If A and B are two perpendicular vectors, then AB=.


Given the vector v=7,2 and the vector u=3,6, find uv.


Given that 𝐴𝐵=(5,12), find 𝐴𝐵𝐴𝐵.


If the two vectors A=5,10 and B=2,𝑘 are perpendicular, determine the value of 𝑘.

  • A𝑘=25
  • B𝑘=4
  • C𝑘=1
  • D𝑘=1
  • E𝑘=25


Given that A=4,𝑘, B=12,3, and AB, determine the value of 𝑘.

  • A𝑘=16
  • B𝑘=16
  • C𝑘=9
  • D𝑘=1
  • E𝑘=9


If A, B, and C are unit vectors, such that ABCO++=, find the value of ABBCCA++.

  • A12
  • B32
  • C12
  • D3
  • E32


If A and B are unit vectors, which interval does AB lie in?

  • A[1,1]
  • B(0,1)
  • C(1,1)
  • D


Square 𝐴𝐵𝐶𝐷 has side 10 cm. What is 𝐴𝐵𝐵𝐶?


In trapezoid 𝐴𝐵𝐶𝐷, with parallel sides 𝐴𝐷 and 𝐵𝐶, suppose 𝐴 and 𝐵 are right angles, and that 𝐴𝐷=12𝐵𝐶=27, while 𝐶𝐷=33. Provide the exact value of 𝐶𝐷𝐶𝐵.


Given that 𝐴𝐵𝐶 is an isosceles triangle, where 𝐴𝐵=𝐴𝐶=6cm and 𝑚𝐴=120, determine 𝐶𝐴𝐵𝐶.

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