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Lesson: Dot Product

Sample Question Videos

Worksheet • 25 Questions • 1 Video

Q1:

If ⃑ 𝐴 and ⃑ 𝐡 are unit vectors, which interval does ⃑ 𝐴 β‹… ⃑ 𝐡 lie in?

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

Q2:

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

Q3:

If ο€Ί ⃑ 𝐴 + ⃑ 𝐡  β‹… ο€Ί ⃑ 𝐴 βˆ’ ⃑ 𝐡  = 5 7 and β€– β€– ⃑ 𝐴 β€– β€– = 3 β€– β€– ⃑ 𝐡 β€– β€– , find β€– β€– ⃑ 𝐴 β€– β€– to the nearest hundredth.

Q4:

In rectangle 𝐴 𝐡 𝐢 𝐷 , we have 𝐴 𝐡 = 1 5 and 𝐡 𝐢 = 1 1 . Determine ο€Ί οƒŸ 𝐡 𝐢  β‹… ο€Ί 5 οƒ  𝐷 𝐡  to the nearest hundredth.

Q5:

⃑ 𝐴 β‹… ⃑ 𝐴 = .

  • A β€– β€– ⃑ 𝐴 β€– β€– 2
  • B βˆ’ 1
  • C0
  • D1
  • E βˆ’ β€– β€– ⃑ 𝐴 β€– β€– 2

Q6:

In trapezium 𝐴 𝐡 𝐢 𝐷 , with parallel sides 𝐴 𝐷 and 𝐡 𝐢 , suppose ∠ 𝐴 and ∠ 𝐡 are right angles, and that 𝐴 𝐡 = 1 2 𝐡 𝐢 = 2 9 . 8 , while 𝐢 𝐷 = 3 9 . Determine οƒ  𝐷 𝐡 β‹… οƒŸ 𝐡 𝐢 .

Q7:

In trapezium 𝐴 𝐡 𝐢 𝐷 , with parallel sides 𝐴 𝐷 and 𝐡 𝐢 , suppose ∠ 𝐴 and ∠ 𝐡 are right angles and that 𝐴 𝐡 = 1 2 𝐡 𝐢 = 3 7 , while 𝐢 𝐷 = 3 9 . Determine οƒ  𝐷 𝐢 β‹… οƒ  𝐴 𝐡 .

Q8:

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

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

Q9:

If find .

Q10:

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

Q11:

If ⃑ 𝐴 = 2 ⃑ 𝑖 and ⃑ 𝐡 = ⃑ 𝑖 βˆ’ 9 ⃑ 𝑗 , calculate the scalar product of ⃑ 𝐴 and ⃑ 𝐡 .

Q12:

and Find ⃑ 𝐴 β‹… ⃑ 𝐡 .

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 βŠ™ .

  • A 4 2 √ 2 Nβ‹…m
  • B βˆ’ 4 2 √ 2 Nβ‹…m
  • C βˆ’ 1 2 √ 2 Nβ‹…m
  • D 1 2 √ 2 Nβ‹…m

Q14:

If β€– β€– ⃑ 𝐴 β€– β€– = 1 7 , β€– β€– ⃑ 𝐡 β€– β€– = 1 2 , and ⃑ 𝐴 βŠ™ ⃑ 𝐡 = 1 0 2 , find the measure of the angle between the two vectors.

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

Q15:

𝐴 𝐡 𝐢 𝐷 is a trapezium, where 𝐴 𝐷 βˆ₯ 𝐡 𝐢 , π‘š ∠ 𝐴 = π‘š ∠ 𝐡 = 9 0 ∘ , 𝐴 𝐷 = 1 2 𝐡 𝐢 = 2 0 c m , and 𝐢 𝐷 = 2 2 c m , evaluate οƒ  𝐡 𝐷 βŠ™ οƒ  𝐡 𝐴 .

Q16:

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.

Q17:

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.

Q18:

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  .

  • A894.01
  • B 1 548.47
  • C447.01
  • D 1 788.02

Q19:

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

Q20:

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

Q21:

For the unit vectors ⃑ 𝑖 , ⃑ 𝑗 , ⃑ π‘˜ , what is ⃑ 𝑗 β‹… ⃑ 𝑗 ?

Q22:

For the unit vectors ⃑ 𝑖 , ⃑ 𝑗 , ⃑ π‘˜ , what is ⃑ 𝑖 β‹… ⃑ 𝑗 ?

Q23:

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

Q24:

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 .

Q25:

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’ 1 3 5 . 3 7 5
  • B135.375
  • C βˆ’ 2 7 0 . 7 5
  • D270.75
  • E βˆ’ 5 4 1 . 5
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