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 26.

  • A 1 0 1 0 3
  • B 1 2 0 3 2 0
  • C 1 0 1 0 3 1 0 1 0
  • D 1 1
  • E 2 8 6 8

Q2:

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

  • A 3 2 + 5 2 i j
  • B 3 3 4 3 4 + 5 3 4 3 4 i j
  • C 3 3 4 3 4 + 5 3 4 3 4 i j
  • D 3 3 4 + 5 3 4 i j
  • E 3 2 2 + 5 2 2 i j

Q3:

Which of these vectors has the greatest magnitude?

  • A 3 i k
  • B i j k +
  • C i j +
  • D 2 + 3 i j k
  • E 3 2 i k

Q4:

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

  • A 1 , 0 , 0
  • B 1 7 1 7 , 0 , 4 1 7 1 7
  • C 1 7 , 0 , 4 1 7
  • D 1 7 1 7 , 0 , 4 1 7 1 7
  • E 1 7 , 0 , 4 1 7

Q5:

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

  • A 3
  • B 3 ( ) i j k
  • C 3 ( + + ) i j k
  • D 3 3 ( + + ) i j k
  • E 3 3 ( ) i j k

Q6:

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

  • A 0 , 4 5 , 8 5
  • B 1 1 , 1 1 , 3 1 1
  • C 1 1 1 1 , 1 1 1 1 , 3 1 1 1 1
  • D 0 , 5 5 , 0
  • E 0 , 5 5 , 2 5 5

Q7:

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

Q8:

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

  • A 2 2 ( 2 + 2 ) i k
  • B 2 2 ( 2 + 2 ) i k
  • C 2 4 ( 2 + 2 ) i k
  • D 6 6 ( + 2 ) i j k
  • E 2 4 ( 2 + 2 ) i k

Q9:

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

  • A 5 , 8
  • B 8 , 5
  • C 1 5 , 6
  • D 6 , 1 5
  • E 6 , 5

Q10:

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

  • A 1 2 , 2 2
  • B 1 2 , 1 1
  • C 6 , 1 1
  • D 3 , 1 1
  • E 3 , 5 . 5

Q11:

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

  • A 8 , 1 2
  • B 1 2 , 8
  • C 1 2 , 8
  • D 1 2 , 8
  • E 1 2 , 8

Q12:

𝐴 is represented by the following graph.

Which of the following graphs represents 12𝐴?

  • A
  • B
  • C
  • D
  • E

Q13:

𝐴 is represented by the following graph.

Which of the following graphs represents 2𝐴?

  • A
  • B
  • C
  • D
  • E

Q14:

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

  • A 3 5 , 4 5
  • B 4 5 , 3 5
  • C 5 4 , 5 3
  • D 5 3 , 5 4
  • E5

Q15:

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

  • A 1 3 1 2 , 5 1 2
  • B 1 2 1 3 , 5 1 3
  • C 1 2 5 , 1 3 5
  • D 1 3 1 2 , 1 3 5
  • E 5 1 3 , 1 2 1 3

Q16:

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

  • A 1 , 2 4
  • B 2 4 , 3
  • C 3 , 2 4
  • D 3 , 8

Q17:

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

  • A
  • B
  • C
  • D
  • E

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