Lesson Worksheet: Dot Product in 2D Mathematics

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

Q1:

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

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

Q2:

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

Q3:

If (+)⋅(−)=57ABAB and ||=3||AB, find ||A to the nearest hundredth.

Q4:

In rectangle 𝐴𝐵𝐶𝐷, we have 𝐴𝐵=15 and 𝐵𝐶=11. Determine 𝐵𝐶⋅5𝐷𝐵 to the nearest hundredth.

Q5:

AA⋅=.

  • A−1
  • B0
  • C1
  • D||A
  • E−||A

Q6:

In trapezoid 𝐴𝐵𝐶𝐷, with parallel sides 𝐴𝐷 and 𝐵𝐶, suppose ∠𝐴 and ∠𝐵 are right angles, and that 𝐴𝐵=12𝐵𝐶=29.8, while 𝐶𝐷=39. Determine 𝐷𝐵⋅𝐵𝐶.

Q7:

In trapezoid 𝐴𝐵𝐶𝐷, with parallel sides 𝐴𝐷 and 𝐵𝐶, suppose ∠𝐴 and ∠𝐵 are right angles and that 𝐴𝐵=12𝐵𝐶=37, while 𝐶𝐷=39. Determine 𝐷𝐶⋅𝐴𝐵.

Q8:

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.

Q9:

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

Q10:

If Ai=2 and Bij=−9, calculate the scalar product of A and B.

Q11:

Given that the norm of A is 4 newtons in the direction of 45∘north of west, and the norm of B is 21 meters in the direction of west, determine AB⊙.

  • A42√2 N⋅m
  • B12√2 N⋅m
  • C−42√2 N⋅m
  • D−12√2 N⋅m

Q12:

𝐴𝐵𝐶𝐷 is a trapezoid, where 𝐴𝐷∥𝐵𝐶, 𝑚∠𝐴=𝑚∠𝐵=90∘, 𝐴𝐷=12𝐵𝐶=20cm, and 𝐶𝐷=22cm, evaluate 𝐵𝐷⊙𝐵𝐴.

Q13:

Given that 𝐴𝐵𝐶 is an isosceles triangle, where 𝐴𝐵=𝐴𝐶=19cm and 𝑚∠𝐴=51∘, determine 𝐵𝐴⋅𝐵𝐶 correct to the nearest hundredth.

Q14:

If 𝐴𝐵𝐶 is an equilateral triangle of side 4.75, find 𝐴𝐵⋅𝐴𝐶 approximated to the nearest hundredth.

Q15:

If 𝐴𝐵𝐶 is an equilateral triangle of side length 29.9 cm, find 𝐴𝐵⋅𝐴𝐶+𝐶𝐵.

Q16:

Equilateral triangle 𝐴𝐵𝐶 has side 6.6. Find 6𝐴𝐶⋅5𝐶𝐵.

Q17:

Equilateral triangle 𝐴𝐵𝐶 has side 46.6. Find 𝐴𝐵⋅𝐵𝐶 to the nearest hundredth.

Q18:

If 𝐴𝐵𝐶𝐷 is a parallelogram in which 𝑚∠𝐵𝐴𝐶=90∘, 𝐴𝐵=18cm, and 𝐵𝐶=26cm, evaluate 310𝐷𝐶⊙−12𝐶𝐵.

Q19:

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

Q20:

Given that 𝐴𝐵𝐶 is an equilateral triangle whose side length is 57 cm, and 𝑀 is the point of concurrency of its medians, evaluate 𝑀𝐷⊙𝑀𝐹.

Q21:

Given that 𝐴𝐵𝐶 is a right triangle at 𝐵, where 𝐴𝐵=9cm and 𝐵𝐶=16cm, determine 910𝐶𝐴⊙−110𝐴𝐵.

Q22:

𝐴𝐵𝐶𝐷 is a square with a side length of 9.9. Find 𝐴𝐵⋅𝐷𝐶.

Q23:

𝐴𝐵𝐶𝐷 is a square that has a side length of 12 cm. Determine the scalar product of the two vectors 𝐷𝐶 and 𝐷𝐵.

Q24:

Given that 𝐴𝐵𝐶𝐷𝐸𝐹 is a regular hexagon of side length 8 cm, evaluate (𝐵𝐷+𝐹𝐴)⊙𝐴𝐵.

Q25:

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

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