Worksheet: Dot Product

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In this worksheet, we will practice using the dot product to find the magnitude of a vector.

Q1:

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

  • A ] 0 , 1 [
  • B ] − 1 , 1 [
  • C ℝ +
  • D [ − 1 , 1 ]

Q2:

Square 𝐴 𝐵 𝐶 𝐷 has side 10 cm. What is 𝐴 𝐵 ⋅ 𝐵 𝐶 ?

Q3:

If ⃑ 𝐴 + ⃑ 𝐵 ⋅ ⃑ 𝐴 − ⃑ 𝐵 = 5 7 and ‖ ‖ ⃑ 𝐴 ‖ ‖ = 3 ‖ ‖ ⃑ 𝐵 ‖ ‖ , find ‖ ‖ ⃑ 𝐴 ‖ ‖ to the nearest hundredth.

Q4:

In rectangle 𝐴 𝐵 𝐶 𝐷 , we have 𝐴 𝐵 = 1 5 and 𝐵 𝐶 = 1 1 . Determine 𝐵 𝐶 ⋅ 5 𝐷 𝐵 to the nearest hundredth.

Q5:

⃑ 𝐴 ⋅ ⃑ 𝐴 = .

  • A − ‖ ‖ ⃑ 𝐴 ‖ ‖ 2
  • B0
  • C1
  • D ‖ ‖ ⃑ 𝐴 ‖ ‖ 2
  • E − 1

Q6:

In trapezium 𝐴 𝐵 𝐶 𝐷 , with parallel sides 𝐴 𝐷 and 𝐵 𝐶 , suppose ∠ 𝐴 and ∠ 𝐵 are right angles, and that 𝐴 𝐵 = 1 2 𝐵 𝐶 = 2 9 . 8 , while 𝐶 𝐷 = 3 9 . Determine 𝐷 𝐵 ⋅ 𝐵 𝐶 .

Q7:

In trapezium 𝐴 𝐵 𝐶 𝐷 , with parallel sides 𝐴 𝐷 and 𝐵 𝐶 , suppose ∠ 𝐴 and ∠ 𝐵 are right angles and that 𝐴 𝐵 = 1 2 𝐵 𝐶 = 3 7 , while 𝐶 𝐷 = 3 9 . Determine 𝐷 𝐶 ⋅ 𝐴 𝐵 .

Q8:

In trapezoid , with parallel sides and , suppose and are right angles, and that , while . Determine .

  • A
    2 916
  • B
    1 024.58
  • C364.5
  • D
    1 458

Q9:

If find .

Q10:

If the two vectors and are perpendicular, determine the value of .

Q11:

If ⃑ 𝐴 = 2 ⃑ 𝑖 and ⃑ 𝐵 = ⃑ 𝑖 − 9 ⃑ 𝑗 , calculate the scalar product of ⃑ 𝐴 and ⃑ 𝐵 .

Q12:

and Find ⃑ 𝐴 ⋅ ⃑ 𝐵 .

Q13:

Given that the norm of A is 4 newtons in the direction of 4 5 ∘ north of west, and the norm of B is 21 meters in the direction of west, determine A B ⊙ .

  • A 1 2 √ 2 N⋅m
  • B − 4 2 √ 2 N⋅m
  • C − 1 2 √ 2 N⋅m
  • D 4 2 √ 2 N⋅m

Q14:

If | | = 1 7 A , | | = 1 2 B , and A B ⊙ = 1 0 2 , find the measure of the angle between the two vectors.

  • A 3 0 ∘
  • B 1 5 0 ∘
  • C 1 2 0 ∘
  • D 6 0 ∘

Q15:

𝐴 𝐵 𝐶 𝐷 is a trapezium, where 𝐴 𝐷 ∥ 𝐵 𝐶 , 𝑚 ∠ 𝐴 = 𝑚 ∠ 𝐵 = 9 0 ∘ , 𝐴 𝐷 = 1 2 𝐵 𝐶 = 2 0 c m , and 𝐶 𝐷 = 2 2 c m , evaluate 𝐵 𝐷 ⊙ 𝐵 𝐴 .

Q16:

Given that 𝐴 𝐵 𝐶 is an isosceles triangle, where 𝐴 𝐵 = 𝐴 𝐶 = 1 9 c m and 𝑚 ∠ 𝐴 = 5 1 ∘ , determine 𝐵 𝐴 ⋅ 𝐵 𝐶 correct to the nearest hundredth.

Q17:

If 𝐴 𝐵 𝐶 is an equilateral triangle of side 4.75, find 𝐴 𝐵 ⋅ 𝐴 𝐶 approximated to the nearest hundredth.

Q18:

If 𝐴 𝐵 𝐶 is an equilateral triangle of side length 29.9 cm, find 𝐴 𝐵 ⋅ 𝐴 𝐶 + 𝐶 𝐵 .

  • A 1 788.02
  • B 1 548.47
  • C447.01
  • D894.01

Q19:

Equilateral triangle 𝐴 𝐵 𝐶 has side 6.6. Find 6 𝐴 𝐶 ⋅ 5 𝐶 𝐵 .

Q20:

Equilateral triangle 𝐴 𝐵 𝐶 has side 46.6. Find 𝐴 𝐵 ⋅ 𝐵 𝐶 to the nearest hundredth.

Q21:

For the unit vectors ⃑ 𝑖 , ⃑ 𝑗 , ⃑ 𝑘 , what is ⃑ 𝑗 ⋅ ⃑ 𝑗 ?

Q22:

For the unit vectors ⃑ 𝑖 , ⃑ 𝑗 , ⃑ 𝑘 , what is ⃑ 𝑖 ⋅ ⃑ 𝑗 ?

Q23:

If is a parallelogram in which , , and , evaluate .

Q24:

Given that 𝐴 𝐵 𝐶 is an isosceles triangle, where 𝐴 𝐵 = 𝐴 𝐶 = 6 c m and 𝑚 ∠ 𝐴 = 1 2 0 ∘ , determine 𝐶 𝐴 ⊙ 𝐵 𝐶 .

Q25:

Given that 𝐴 𝐵 𝐶 is an equilateral triangle whose side length is 57 cm, and 𝑀 is the point of concurrency of its medians, evaluate 𝑀 𝐷 ⊙ 𝑀 𝐹 .

  • A − 5 4 1 . 5
  • B − 2 7 0 . 7 5
  • C270.75
  • D − 1 3 5 . 3 7 5
  • E135.375

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