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

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

Q1:

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

Q2:

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

Q3:

Given that 𝐴𝐵=(5,12), find 𝐴𝐵⋅𝐴𝐵.

Q4:

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

Q5:

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

Q6:

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

  • A−12
  • B−32
  • C12
  • D−3
  • E32

Q7:

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

  • A[−1,1]
  • B(0,1)
  • C(−1,1)
  • Dℝ

Q8:

Square 𝐴𝐵𝐶𝐷 has side 10 cm. What is 𝐴𝐵⋅𝐵𝐶?

Q9:

In trapezoid 𝐴𝐵𝐶𝐷, with parallel sides 𝐴𝐷 and 𝐵𝐶, suppose ∠𝐴 and ∠𝐵 are right angles, and that 𝐴𝐷=12𝐵𝐶=27, while 𝐶𝐷=33. Determine 𝐶𝐷⋅𝐶𝐵.

Q10:

Given that 𝐴𝐵𝐶 is an isosceles triangle, where 𝐴𝐵=𝐴𝐶=6cm and 𝑚∠𝐴=120∘, determine 𝐶𝐴⊙𝐵𝐶.

This lesson includes 33 additional questions and 296 additional question variations for subscribers.

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