# 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
• B
• C

Q2:

In the given parallelogram , , is the midpoint of , and is the midpoint of . Complete the following: is equivalent to . • A
• B
• C
• D

Q3:

Find the components of the vector shown on the grid of unit squares below. • A
• B
• C
• D
• E

Q4:

Find the magnitude of the vector shown on the grid of unit squares below. Q5:

Find the magnitude of the vector shown on the grid of unit squares below. • A5
• B
• C9
• D
• E

Q6:

Find the magnitude of the vector shown on the grid of unit squares below. • A
• B
• C13
• D
• E

Q7:

Given that is a square of side length 9 cm, determine the scalar product of and .

Q8:

The vector describes a translation from point to point . What is another way of writing the vector ?

• A
• B
• C
• D
• E

Q9:

What is the terminal point of the vector ?

• A
• B
• C
• D
• E

Q10:

What shape is formed by these vectors? • Aa parallelogram
• Ba rectangle
• Ca rhombus
• Da kite
• Ea square

Q11:

In the given figure, and are parallel lines; however, is NOT parallel to either or . Given that , , and , determine whether and are in the same, opposite, or different directions. • Bsame
• Copposite

Q12:

Given that , , and , determine the values of and .

• A,
• B,
• C,
• D,

Q13:

The given diagram shows the vectors and . Two more vectors are drawn: a vector equivalent to with initial point and a vector equivalent to with initial point .

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

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

Q14:

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

• AThe intial point of is the terminal point of .
• B and have the same terminal point.
• C
• DThe intial point of is the terminal point of .
• E and have the same initial point.