Worksheet: Scalars, Vectors, and Directed Line Segments

In this worksheet, we will practice recognizing, constructing, and expressing directed line segments.

Q1:

Which vector has the same direction as a ?

  • A b
  • B d
  • C c

Q2:

In the given parallelogram 𝐴 𝐵 𝐶 𝐷 , 𝐴 𝐶 𝐵 𝐷 = { 𝑀 } , 𝐸 is the midpoint of 𝐴 𝐵 , and 𝐹 is the midpoint of 𝐵 𝐶 . Complete the following: 1 2 𝐴 𝐶 is equivalent to .

  • A 𝑀 𝐷
  • B 𝐴 𝑀
  • C 𝑀 𝐴
  • D 𝐷 𝑀

Q3:

Find the components of the vector v shown on the grid of unit squares below.

  • A 6 , 0
  • B 0 , 6
  • C 0 , 6
  • D 6 , 0
  • E 6 , 1

Q4:

Find the magnitude of the vector v shown on the grid of unit squares below.

Q5:

Find the magnitude of the vector v shown on the grid of unit squares below.

  • A 3
  • B 5
  • C5
  • D 2
  • E9

Q6:

Find the magnitude of the vector v shown on the grid of unit squares below.

  • A13
  • B 3
  • C 2
  • D 1 3
  • E 5

Q7:

Given that 𝐴 𝐵 𝐶 𝐷 is a square of side length 9 cm, determine the scalar product of 2 𝐷 𝐵 and 3 5 𝐵 𝐴 .

Q8:

The vector u describes a translation from point 𝐴 to point 𝐵 .

What is another way of writing the vector u ?

  • A A
  • B 𝐵 𝐴
  • C 𝐴 𝐵
  • D B
  • E 𝐴 𝐵

Q9:

What is the terminal point of the vector 𝐴 𝐵 ?

  • A 𝐵
  • B 𝐴 𝐵
  • C 𝐴
  • D 𝐴 + 𝐵
  • E 𝐵 𝐴

Q10:

What shape is formed by these vectors?

  • Aa parallelogram
  • Ba rhombus
  • Ca rectangle
  • Da kite
  • Ea square

Q11:

In the given figure, 𝐴 𝐵 and 𝐶 𝐷 are parallel lines; however, 𝑋 𝑌 is NOT parallel to either 𝐴 𝐵 or 𝐶 𝐷 . Given that 𝐸 𝐴 𝐵 , 𝐹 𝐶 𝐷 , and 𝑍 𝑋 𝑌 , determine whether 𝑌 𝑍 and 𝑋 𝑍 are in the same, opposite, or different directions.

  • Adifferent
  • Bopposite
  • Csame

Q12:

Given that A = 𝑘 , 4 , B = 4 , 𝑚 , and A B = 2 , determine the values of 𝑘 and 𝑚 .

  • A 𝑘 = 8 , 𝑚 = 8
  • B 𝑘 = 8 , 𝑚 = 2
  • C 𝑘 = 8 , 𝑚 = 2
  • D 𝑘 = 8 , 𝑚 = 8

Q13:

The given diagram shows the vectors 𝐴 𝐵 and 𝐴 𝐶 .

Two more vectors are drawn: a vector equivalent to 𝐴 𝐶 with initial point 𝐵 and a vector equivalent to 𝐴 𝐵 with initial point 𝐶 .

What can you say about the terminal points of these vectors?

  • AThey are the same point.
  • BThey lie on the angle bisector of 𝐵 𝐴 𝐶 .
  • CThey are twice as far away from each other as 𝐵 is from 𝐶 .
  • DThey are the same distance from each other as 𝐵 is from 𝐶 .
  • EThey lie on the line 𝐵 𝐶 .

Q14:

Select all the statements that must be true if u and v are equivalent vectors.

  • A u and v have the same initial point.
  • B | | = | | u v
  • CThe intial point of u is the terminal point of v .
  • D u and v have the same terminal point.
  • E The intial point of v is the terminal point of u .

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