Worksheet: Dot Product

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

Q1:

If āƒ‘ š“ and āƒ‘ šµ are unit vectors, which interval does āƒ‘ š“ ā‹… āƒ‘ šµ lie in?

  • A ] 0 , 1 [
  • B ] āˆ’ 1 , 1 [
  • C ā„ +
  • D [ āˆ’ 1 , 1 ]

Q2:

Square š“ šµ š¶ š· has side 10 cm. What is ļƒ  š“ šµ ā‹… ļƒŸ šµ š¶ ?

Q3:

If ļ€ŗ āƒ‘ š“ + āƒ‘ šµ ļ† ā‹… ļ€ŗ āƒ‘ š“ āˆ’ āƒ‘ šµ ļ† = 5 7 and ā€– ā€– āƒ‘ š“ ā€– ā€– = 3 ā€– ā€– āƒ‘ šµ ā€– ā€– , find ā€– ā€– āƒ‘ š“ ā€– ā€– to the nearest hundredth.

Q4:

In rectangle š“ šµ š¶ š· , we have š“ šµ = 1 5 and šµ š¶ = 1 1 . Determine ļ€ŗ ļƒŸ šµ š¶ ļ† ā‹… ļ€ŗ 5 ļƒ  š· šµ ļ† to the nearest hundredth.

Q5:

āƒ‘ š“ ā‹… āƒ‘ š“ = .

  • A āˆ’ ā€– ā€– āƒ‘ š“ ā€– ā€– 2
  • B0
  • C1
  • D ā€– ā€– āƒ‘ š“ ā€– ā€– 2
  • E āˆ’ 1

Q6:

In trapezium š“ šµ š¶ š· , with parallel sides š“ š· and šµ š¶ , suppose āˆ  š“ and āˆ  šµ are right angles, and that š“ šµ = 1 2 šµ š¶ = 2 9 . 8 , while š¶ š· = 3 9 . Determine ļƒ  š· šµ ā‹… ļƒŸ šµ š¶ .

Q7:

In trapezium š“ šµ š¶ š· , with parallel sides š“ š· and šµ š¶ , suppose āˆ  š“ and āˆ  šµ are right angles and that š“ šµ = 1 2 šµ š¶ = 3 7 , while š¶ š· = 3 9 . Determine ļƒ  š· š¶ ā‹… ļƒ  š“ šµ .

Q8:

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

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

Q9:

If find .

Q10:

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

Q11:

If āƒ‘ š“ = 2 āƒ‘ š‘– and āƒ‘ šµ = āƒ‘ š‘– āˆ’ 9 āƒ‘ š‘— , calculate the scalar product of āƒ‘ š“ and āƒ‘ šµ .

Q12:

and Find āƒ‘ š“ ā‹… āƒ‘ šµ .

Q13:

Given that the norm of A is 4 newtons in the direction of 4 5 āˆ˜ north of west, and the norm of B is 21 meters in the direction of west, determine A B āŠ™ .

  • A 1 2 āˆš 2 Nā‹…m
  • B āˆ’ 4 2 āˆš 2 Nā‹…m
  • C āˆ’ 1 2 āˆš 2 Nā‹…m
  • D 4 2 āˆš 2 Nā‹…m

Q14:

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

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

Q15:

š“ šµ š¶ š· is a trapezium, where š“ š· āˆ„ šµ š¶ , š‘š āˆ  š“ = š‘š āˆ  šµ = 9 0 āˆ˜ , š“ š· = 1 2 šµ š¶ = 2 0 c m , and š¶ š· = 2 2 c m , evaluate ļƒ  šµ š· āŠ™ ļƒ  šµ š“ .

Q16:

Given that š“ šµ š¶ is an isosceles triangle, where š“ šµ = š“ š¶ = 1 9 c m and š‘š āˆ  š“ = 5 1 āˆ˜ , determine ļƒ  šµ š“ ā‹… ļƒŸ šµ š¶ correct to the nearest hundredth.

Q17:

If š“ šµ š¶ is an equilateral triangle of side 4.75, find ļƒ  š“ šµ ā‹… ļƒ  š“ š¶ approximated to the nearest hundredth.

Q18:

If š“ šµ š¶ is an equilateral triangle of side length 29.9 cm, find ļƒ  š“ šµ ā‹… ļ€ŗ ļƒ  š“ š¶ + ļƒŸ š¶ šµ ļ† .

  • A 1ā€‰788.02
  • B 1ā€‰548.47
  • C447.01
  • D894.01

Q19:

Equilateral triangle š“ šµ š¶ has side 6.6. Find ļ€ŗ 6 ļƒ  š“ š¶ ļ† ā‹… ļ€ŗ 5 ļƒŸ š¶ šµ ļ† .

Q20:

Equilateral triangle š“ šµ š¶ has side 46.6. Find ļƒ  š“ šµ ā‹… ļƒŸ šµ š¶ to the nearest hundredth.

Q21:

For the unit vectors āƒ‘ š‘– , āƒ‘ š‘— , āƒ‘ š‘˜ , what is āƒ‘ š‘— ā‹… āƒ‘ š‘— ?

Q22:

For the unit vectors āƒ‘ š‘– , āƒ‘ š‘— , āƒ‘ š‘˜ , what is āƒ‘ š‘– ā‹… āƒ‘ š‘— ?

Q23:

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

Q24:

Given that š“ šµ š¶ is an isosceles triangle, where š“ šµ = š“ š¶ = 6 c m and š‘š āˆ  š“ = 1 2 0 āˆ˜ , determine ļƒ  š¶ š“ āŠ™ ļƒŸ šµ š¶ .

Q25:

Given that š“ šµ š¶ is an equilateral triangle whose side length is 57 cm, and š‘€ is the point of concurrency of its medians, evaluate ļƒ  š‘€ š· āŠ™ ļƒ  š‘€ š¹ .

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

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