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?

  • Ad
  • Bb
  • Cc

Q2:

In the given parallelogram 𝐴𝐵𝐶𝐷, 𝐴𝐶𝐵𝐷={𝑀}, 𝐸 is the midpoint of 𝐴𝐵, and 𝐹 is the midpoint of 𝐵𝐶. Complete the following: 12𝐴𝐶 is equivalent to .

  • A𝐴𝑀
  • B𝑀𝐴
  • C𝐷𝑀
  • D𝑀𝐷

Q3:

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

  • A6,0
  • B0,6
  • C6,0
  • D0,6
  • E6,1

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.

  • A5
  • B3
  • C9
  • D5
  • E2

Q6:

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

  • A3
  • B13
  • C13
  • D2
  • E5

Q7:

Given that 𝐴𝐵𝐶𝐷 is a square of side length 9 cm, determine the scalar product of 2𝐷𝐵 and 35𝐵𝐴.

Q8:

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

What is another way of writing the vector u?

  • AB
  • B𝐴𝐵
  • C𝐴𝐵
  • DA
  • E𝐵𝐴

Q9:

What is the terminal point of the vector 𝐴𝐵?

  • A𝐴+𝐵
  • B𝐴
  • C𝐵𝐴
  • D𝐵
  • E𝐴𝐵

Q10:

What shape is formed by these vectors?

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

Q11:

In the given figure, 𝐴𝐵 and 𝐶𝐷 are parallel lines; however, 𝑋𝑌 is NOT parallel to either 𝐴𝐵 or 𝐶𝐷. Given that 𝐸𝐴𝐵, 𝐹𝐶𝐷, and 𝑍𝑋𝑌, determine whether 𝑌𝑍 and 𝑋𝑍 are in the same, opposite, or different directions.

  • Adifferent
  • Bsame
  • Copposite

Q12:

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

  • A𝑘=8, 𝑚=2
  • B𝑘=8, 𝑚=8
  • C𝑘=8, 𝑚=2
  • D𝑘=8, 𝑚=8

Q13:

The given diagram shows the vectors 𝐴𝐵 and 𝐴𝐶.

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

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

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

Q14:

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

  • AThe intial point of v is the terminal point of u.
  • Bu and v have the same terminal point.
  • C||=||uv
  • DThe intial point of u is the terminal point of v.
  • Eu and v have the same initial point.

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