Worksheet: Scalar Multiplication and Unit Vectors

In this worksheet, we will practice multiplying a vector by a scalar and how to find a unit vector in the direction of any given vector by dividing the vector by a scalar.

Q1:

Find the unit vector in the same direction as the vector 3+5ij.

  • A32+52ij
  • B33434+53434ij
  • C33434+53434ij
  • D334+534ij
  • E322+522ij

Q2:

Find the unit vector in the direction of 𝐴𝐵, given A0,1,2 and B1,1,2.

  • A1,0,0
  • B1717,0,41717
  • C17,0,417
  • D1717,0,41717
  • E17,0,417

Q3:

Find the unit vector in the same direction as the vector ijk.

  • A3
  • B3()ijk
  • C3(++)ijk
  • D33(++)ijk
  • E33()ijk

Q4:

Given A=2,0,2 and B=1,1,1, determine the unit vector in the direction 2BA.

  • A0,45,85
  • B11,11,311
  • C1111,1111,31111
  • D0,55,0
  • E0,55,255

Q5:

Consider the vector Aijk=524. Is the unit vector in the direction of A the same as the unit vector in the direction of 3A?

  • AYes
  • BNo

Q6:

Given that Aijk=2+ and Bjk=+, find the unit vector in the direction of BA.

  • A22(2+2)ik
  • B22(2+2)ik
  • C24(2+2)ik
  • D66(+2)ijk
  • E24(2+2)ik

Q7:

Given that A=2,5, find 3A.

  • A5,8
  • B8,5
  • C15,6
  • D6,15
  • E6,5

Q8:

Given that A=6,11, find 12A.

  • A12,22
  • B12,11
  • C6,11
  • D3,11
  • E3,5.5

Q9:

Given that A=3,2, find 4A.

  • A8,12
  • B12,8
  • C12,8
  • D12,8
  • E12,8

Q10:

𝐴 is represented by the following graph.

Which of the following graphs represents 12𝐴?

  • A
  • B
  • C
  • D
  • E

Q11:

𝐴 is represented by the following graph.

Which of the following graphs represents 2𝐴?

  • A
  • B
  • C
  • D
  • E

Q12:

What is the unit vector in the same direction as A=3,4?

  • A35,45
  • B45,35
  • C54,53
  • D53,54
  • E5

Q13:

Determine the unit vector of vector A from the following graph.

  • A1312,512
  • B1213,513
  • C125,135
  • D1312,135
  • E513,1213

Q14:

Given that A=1,8, find 3A.

  • A1,24
  • B24,3
  • C3,24
  • D3,8

Q15:

Given that A is represented by the graph shown, which of the following represents 3A?

  • A
  • B
  • C
  • D
  • E

Q16:

All of the following are unit vectors except .

  • A1,0
  • B0.6,0.8
  • C0,1
  • D1,1

Q17:

Find the unit vector in the direction of 𝑃𝑄.

  • A889,589
  • B213,313
  • C213,313
  • D889,589
  • E589,889

Q18:

Given points 𝐴(1,10,1) and 𝐵(1,0,2), find point 𝐶 such that 𝐴𝐶=2𝐵𝐶.

  • A(1,10,3)
  • B23,103,3
  • C1,5,32
  • D(2,10,3)
  • E(1,20,1)

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