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Worksheet: Vectors in Terms of Fundamental Unit Vectors

Q1:

Find the unit vector in the direction of the -axis.

  • A
  • B
  • C
  • D
  • E

Q2:

Given that and are two unit vectors, and , evaluate .

Q3:

Find the unit vector in the direction of the -axis.

  • A
  • B
  • C
  • D
  • E

Q4:

Suppose that , , and . What is ?

  • A
  • B
  • C
  • D

Q5:

Suppose that , , and . What is ?

  • A
  • B
  • C
  • D

Q6:

Given that A i j k = 3 + + π‘š and that B is a unit vector equal to 1 5 A , determine the possible values of π‘š .

  • A √ 1 5 5 , βˆ’ √ 1 5 5
  • B 1 5 , βˆ’ 1 5
  • C 3 5 , βˆ’ 3 5
  • D √ 1 5 , βˆ’ √ 1 5

Q7:

Is a unit vector?

  • AFalse
  • BTrue

Q8:

Find the unit vector in the direction of the -axis.

  • A
  • B
  • C
  • D
  • E

Q9:

If A and B are unit vectors and πœƒ the measure of the angle between them, find | ( βˆ’ ) Γ— ( + ) | A B A B .

  • A 𝐴 𝐡 πœƒ 2 2 s i n
  • B s i n πœƒ
  • C 2 𝐴 𝐡 πœƒ s i n
  • D 2 πœƒ s i n
  • E 𝐴 𝐡 πœƒ s i n

Q10:

Suppose a unit vector is such that . Determine the possible values of .

  • A
  • B
  • C
  • D

Q11:

If A i j k = 4 + 4 βˆ’ 5 and B i k = 3 βˆ’ , determine | βˆ’ | A B .

  • A 3 √ 2
  • B3
  • C √ 3 3

Q12:

If A i j k = 3 βˆ’ βˆ’ 4 and B i j k = βˆ’ 3 + 5 βˆ’ 5 , determine | βˆ’ | A B .

  • A √ 2 6
  • B √ 1 3
  • C √ 7 3

Q13:

If and , determine and .

  • A ,
  • B ,
  • C ,

Q14:

If and , determine and .

  • A ,
  • B ,
  • C ,