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Worksheet: Dot Product

Q1:

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

  • A
  • B
  • C
  • D

Q2:

Given that 𝐴 𝐡 𝐢 is an isosceles triangle, where 𝐴 𝐡 = 𝐴 𝐢 = 1 9 c m and π‘š ∠ 𝐴 = 5 1 ∘ , determine οƒ  𝐡 𝐴 β‹… οƒŸ 𝐡 𝐢 correct to the nearest hundredth.

Q3:

Given that 𝐴 𝐡 𝐢 is an isosceles triangle, where 𝐴 𝐡 = 𝐴 𝐢 = 6 c m and π‘š ∠ 𝐴 = 1 2 0 ∘ , determine οƒ  𝐢 𝐴 βŠ™ οƒŸ 𝐡 𝐢 .

Q4:

Given that 𝐴 𝐡 𝐢 is an equilateral triangle whose side length is 57 cm, and 𝑀 is the point of concurrency of its medians, evaluate οƒ  𝑀 𝐷 βŠ™ οƒ  𝑀 𝐹 .

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

Q5:

For the unit vectors , , , what is ?

Q6:

A A β‹… = .

  • A βˆ’ | | A 2
  • B0
  • C1
  • D | | A 2
  • E βˆ’ 1

Q7:

If find 𝑀 β‹… 𝑀 𝐴 𝐴 .

Q8:

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

Q9:

If and , calculate the scalar product of and .

Q10:

and Find A B β‹… .

Q11:

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

  • A
  • B
    1 499.46
  • C
    1 776.08
  • D

Q12:

If , , and , find the size of the angle between the two vectors.

  • A
  • B
  • C
  • D

Q13:

is a trapezoid, where , , , and , evaluate .

  • A
  • B44
  • C
  • D84

Q14:

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

  • A
  • B480.82
  • C
    2 890
  • D152

Q15:

If 𝐴 𝐡 𝐢 is an equilateral triangle of side 4.75, find οƒ  𝐴 𝐡 β‹… οƒ  𝐴 𝐢 approximated to the nearest hundredth.

Q16:

For the unit vectors , , , what is ?

Q17:

If 𝐴 𝐡 𝐢 is an equilateral triangle of side length 29.9 cm, find οƒ  𝐴 𝐡 β‹… ο€Ί οƒ  𝐴 𝐢 + οƒŸ 𝐢 𝐡  .

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

Q18:

Given that is a right triangle at , where and , determine .

  • A
  • B
  • C2.88
  • D7.29

Q19:

In trapezium 𝐴 𝐡 𝐢 𝐷 , with parallel sides 𝐴 𝐷 and 𝐡 𝐢 , suppose ∠ 𝐴 and ∠ 𝐡 are right angles, and that 𝐴 𝐷 = 1 2 𝐡 𝐢 = 2 7 , while 𝐢 𝐷 = 3 3 . Determine οƒ  𝐢 𝐷 β‹… οƒŸ 𝐢 𝐡 .

Q20:

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

Q21:

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

  • A Nβ‹…m
  • B Nβ‹…m
  • C Nβ‹…m
  • D Nβ‹…m

Q22:

Equilateral triangle 𝐴 𝐡 𝐢 has side 6.6. Find ο€Ί 6 οƒ  𝐴 𝐢  β‹… ο€Ί 5 οƒŸ 𝐢 𝐡  .

Q23:

Square 𝐴 𝐡 𝐢 𝐷 has side 10 cm. What is οƒ  𝐴 𝐡 β‹… οƒŸ 𝐡 𝐢 ?

Q24:

If and , find to the nearest hundredth.

Q25:

Equilateral triangle 𝐴 𝐡 𝐢 has side 46.6. Find οƒ  𝐴 𝐡 β‹… οƒŸ 𝐡 𝐢 to the nearest hundredth.