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Worksheet: Introduction to Vectors

Q1:

The components of the vector u are 1 , 2 as the terminal point of the vector is 1 unit right of the initial point and 2 units up from the initial point. What are the components of the vector v ?

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

Q2:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

  • A ( 1 , 5 )
  • B ( 1 , 2 )
  • C ( 2 , 1 )
  • D ( 5 , 1 )
  • E ( 4 , 1 )

What are the coordinates of its initial point?

  • A ( 1 , 2 )
  • B ( 2 , 1 )
  • C ( 1 , 5 )
  • D ( 5 , 1 )
  • E ( 4 , 1 )

What are the components of the vector?

  • A 1 , 4
  • B 1 , 4
  • C 4 , 1
  • D 5 , 1
  • E 4 , 1

Q3:

The initial point of the vector shown in the diagram is the origin, ( 0 , 0 ) .

What are the coordinates of its terminal point?

  • A ( 1 , 2 )
  • B ( 1 , 2 )
  • C ( 2 , 1 )
  • D ( 2 , 1 )
  • E ( 2 , 1 )

What are the components of the vector?

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

Q4:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

  • A ( 1 , 2 )
  • B ( 2 , 2 )
  • C ( 2 , 2 )
  • D ( 2 , 1 )
  • E ( 0 , 3 )

What are the coordinates of its initial point?

  • A ( 2 , 2 )
  • B ( 2 , 2 )
  • C ( 1 , 2 )
  • D ( 2 , 1 )
  • E ( 0 , 3 )

What are the components of the vector?

  • A 0 , 3
  • B 3 , 0
  • C 0 , 3
  • D 2 , 2
  • E 2 , 1

Q5:

Is it true that two vectors with the same components are always equivalent?

  • Ayes
  • Bno

Q6:

The components of the vector u are 1 , 2 as the terminal point of the vector is 1 unit right of the initial point and 2 units up from the initial point. What are the components of the vector v ?

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

Q7:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

  • A ( 5 , 4 )
  • B ( 1 , 1 )
  • C ( 3 , 4 )
  • D ( 4 , 5 )
  • E ( 4 , 3 )

What are the coordinates of its initial point?

  • A ( 1 , 1 )
  • B ( 3 , 4 )
  • C ( 5 , 4 )
  • D ( 4 , 5 )
  • E ( 4 , 3 )

What are the components of the vector?

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

Q8:

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

  • A 2 , 1
  • B 2 , 4
  • C 1 , 2
  • D 4 , 2
  • E 4 , 6

Q9:

Given that , determine the values of and .

  • A ,
  • B ,
  • C ,

Q10:

The components of the vector u are 1 , 2 as the terminal point of the vector is 1 unit right of the initial point and 2 units up from the initial point. What are the components of the vector v ?

  • A 3 , 5
  • B 3 , 4
  • C 4 , 5
  • D 4 , 3
  • E 3 , 1

Q11:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

  • A ( 4 , 3 )
  • B ( 6 , 1 )
  • C ( 3 , 3 )
  • D ( 3 , 4 )
  • E ( 3 , 3 )

What are the coordinates of its initial point?

  • A ( 6 , 1 )
  • B ( 4 , 3 )
  • C ( 1 , 6 )
  • D ( 3 , 4 )
  • E ( 3 , 3 )

What are the components of the vector?

  • A 3 , 3
  • B 6 , 1
  • C 3 , 3
  • D 3 , 4
  • E 3 , 3

Q12:

Find the components of the vector 𝐴 𝐵 .

  • A 2 . 3 , 3 . 2
  • B 4 . 6 , 2 . 9
  • C 3 . 2 , 2 . 3
  • D 2 . 9 , 4 . 6
  • E 2 . 9 , 4 . 6

Q13:

Suppose . What is the component of along the -axis?

Q14:

Using the given figure, express in terms of and .

  • A
  • B
  • C
  • D
  • E

Q15:

Using the given figure, express in terms of and .

  • A
  • B
  • C
  • D
  • E

Q16:

Using the given figure, express in terms of and .

  • A
  • B
  • C
  • D
  • E

Q17:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

  • A ( 2 , 4 )
  • B ( 1 , 2 )
  • C ( 3 , 1 )
  • D ( 4 , 2 )
  • E ( 3 , 0 )

What are the coordinates of its initial point?

  • A ( 1 , 2 )
  • B ( 2 , 1 )
  • C ( 2 , 4 )
  • D ( 4 , 2 )
  • E ( 3 , 0 )

What are the components of the vector?

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

Q18:

Is it true that two equivalent vectors will always have the same components?

  • Ayes
  • Bno

Q19:

Given that A = 1 , 𝑚 , 𝑛 4 , B = 𝑠 , 2 , 4 𝑛 + 5 , and A B = , determine the values of 𝑠 , 𝑚 , and 𝑛 .

  • A 𝑠 = 1 , 𝑚 = 2 , 𝑛 = 5
  • B 𝑠 = 2 , 𝑚 = 1 , 𝑛 = 1
  • C 𝑠 = 2 , 𝑚 = 1 , 𝑛 = 3
  • D 𝑠 = 1 , 𝑚 = 2 , 𝑛 = 3

Q20:

Express in terms of fundamental unit vectors.

  • A
  • B
  • C
  • D

Q21:

The components of the vector u are 2 , 1 as the terminal point of the vector is 2 units right (2 units left) of the initial point and 1 unit up from the initial point. What are the components of the vector v ?

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

Q22:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

  • A ( 1 , 4 )
  • B ( 1 , 1 )
  • C ( 1 , 1 )
  • D ( 4 , 1 )
  • E ( 5 , 2 )

What are the coordinates of its initial point?

  • A ( 1 , 1 )
  • B ( 1 , 1 )
  • C ( 1 , 4 )
  • D ( 4 , 1 )
  • E ( 5 , 2 )

What are the components of the vector?

  • A 5 , 2
  • B 2 , 5
  • C 5 , 2
  • D 4 , 1
  • E 1 , 1

Q23:

The components of the vector u are 2 , 1 as the terminal point of the vector is 2 units right of the initial point and 1 units up (1 unit down) from the initial point. What are the components of the vector v ?

  • A 2 , 4
  • B 1 , 4
  • C 4 , 2
  • D 1 , 4
  • E 4 , 1

Q24:

The components of the vector u are 2 , 1 as the terminal point of the vector is 2 units right of the initial point and 1 unit up (1 unit down) from the initial point. What are the components of the vector v ?

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

Q25:

The components of the vector u are 1 , 2 as the terminal point of the vector is 1 unit right (1 unit left) of the initial point and 2 units up (2 units down) from the initial point. What are the components of the vector v ?

  • A 4 , 3
  • B 3 , 4
  • C 4 , 3
  • D 4 , 3
  • E 4 , 3