Worksheet: Dot Product

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 )
  • D

Q2:

Square 𝐴𝐵𝐶𝐷 has side 10 cm. What is 𝐴𝐵𝐵𝐶?

Q3:

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

Q4:

In rectangle 𝐴𝐵𝐶𝐷, we have 𝐴𝐵=15 and 𝐵𝐶=11. Determine 𝐵𝐶5𝐷𝐵 to the nearest hundredth.

Q5:

A A = .

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

Q6:

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

Q7:

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

Q8:

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

Q9:

If 𝑀=84, find 𝑀𝑀.

Q10:

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

  • A 𝑘 = 2 5
  • B 𝑘 = 4
  • C 𝑘 = 1
  • D 𝑘 = 1
  • E 𝑘 = 2 5

Q11:

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

Q12:

A = 3 1 and B=34. Find AB.

Q13:

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

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

Q14:

If ||=17A, ||=12B, and AB=102, find the measure of the angle between the two vectors.

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

Q15:

𝐴 𝐵 𝐶 𝐷 is a trapezium, where 𝐴𝐷𝐵𝐶, 𝑚𝐴=𝑚𝐵=90, 𝐴𝐷=12𝐵𝐶=20cm, and 𝐶𝐷=22cm, evaluate 𝐵𝐷𝐵𝐴.

Q16:

Given that 𝐴𝐵𝐶 is an isosceles triangle, where 𝐴𝐵=𝐴𝐶=19cm and 𝑚𝐴=51, determine 𝐵𝐴𝐵𝐶 correct to the nearest hundredth.

Q17:

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

Q18:

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

  • A1,788.02
  • B894.01
  • C447.01
  • D1,548.47

Q19:

Equilateral triangle 𝐴𝐵𝐶 has side 6.6. Find 6𝐴𝐶5𝐶𝐵.

Q20:

Equilateral triangle 𝐴𝐵𝐶 has side 46.6. Find 𝐴𝐵𝐵𝐶 to the nearest hundredth.

Q21:

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

Q22:

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

Q23:

If 𝐴𝐵𝐶𝐷 is a parallelogram in which 𝑚𝐵𝐴𝐶=90, 𝐴𝐵=18cm, and 𝐵𝐶=26cm, evaluate 310𝐷𝐶12𝐶𝐵.

Q24:

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

Q25:

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

  • A270.75
  • B 5 4 1 . 5
  • C 1 3 5 . 3 7 5
  • D 2 7 0 . 7 5
  • E135.375

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