Worksheet: Component Form of a Vector

In this worksheet, we will practice expressing a vector in component form given its initial and terminal points.

Q1:

Find the components of the vector 𝐴 𝐵 , where 𝐴 = ( 4 . 5 , 1 . 2 ) and 𝐵 = ( 4 . 5 , 5 . 7 ) .

  • A 4 . 5 , 1 . 2
  • B 4 . 5 , 0
  • C 4 . 5 , 5 . 7
  • D 0 , 4 . 5
  • E 0 , 4 . 5

Q2:

Find the coordinates of the terminal point of the vector in the given diagram.

  • A
  • B
  • C
  • D
  • E

Q3:

Find the coordinates of the initial point of the vector in the given diagram.

  • A
  • B
  • C
  • D
  • E

Q4:

Find the components of the vector 𝐴 𝐵 , where 𝐴 = ( 1 . 5 , 0 . 3 ) and 𝐵 = ( 1 , 5 ) .

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

Q5:

A vector has components and a terminal point . What is its initial point?

  • A
  • B
  • C
  • D
  • E

Q6:

Find the components of the vector .

  • A
  • B
  • C
  • D
  • E

Q7:

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

What are the coordinates of its terminal point?

  • A
  • B
  • C
  • D
  • E

What are the components of the vector?

  • A
  • B
  • C
  • D
  • E

Q8:

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

What are the coordinates of its terminal point?

  • A
  • B
  • C
  • D
  • E

What are the components of the vector?

  • A
  • B
  • C
  • D
  • E

Q9:

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

What are the coordinates of its terminal point?

  • A
  • B
  • C
  • D
  • E

What are the components of the vector?

  • A
  • B
  • C
  • D
  • E

Q10:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

  • A
  • B
  • C
  • D
  • E

What are the coordinates of its initial point?

  • A
  • B
  • C
  • D
  • E

What are the components of the vector?

  • A
  • B
  • C
  • D
  • E

Q11:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

  • A
  • B
  • C
  • D
  • E

What are the coordinates of its initial point?

  • A
  • B
  • C
  • D
  • E

What are the components of the vector?

  • A
  • B
  • C
  • D
  • E

Q12:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

  • A ( 2 , 4 )
  • B ( 4 , 3 )
  • C ( 3 , 4 )
  • D ( 4 , 2 )
  • E ( 0 , 5 )

What are the coordinates of its initial point?

  • A ( 4 , 3 )
  • B ( 3 , 4 )
  • C ( 2 , 4 )
  • D ( 4 , 2 )
  • E ( 0 , 5 )

What are the components of the vector?

  • A ( 0 , 5 )
  • B ( 5 , 0 )
  • C ( 0 , 5 )
  • D ( 4 , 3 )
  • E ( 4 , 2 )

Q13:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

  • A
  • B
  • C
  • D
  • E

What are the coordinates of its initial point?

  • A
  • B
  • C
  • D
  • E

What are the components of the vector?

  • A
  • B
  • C
  • D
  • E

Q14:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

  • A
  • B
  • C
  • D
  • E

What are the coordinates of its initial point?

  • A
  • B
  • C
  • D
  • E

What are the components of the vector?

  • A
  • B
  • C
  • D
  • E

Q15:

Suppose the coordinates of points and are and respectively. Find the components of the vector in terms of , , , and .

  • A
  • B
  • C
  • D
  • E

Q16:

A vector has components and an initial point . What is its terminal point?

  • A
  • B
  • C
  • D
  • E

Q17:

Find the components of the vector , where and .

  • A
  • B
  • C
  • D
  • E

Q18:

Find the components of the vector .

  • A
  • B
  • C
  • D
  • E

Q19:

Given that the coordinates of 𝐴 and 𝐵 are ( 1 2 , 2 4 ) and ( 3 , 1 6 ) respectively, find | | 𝐴 𝐵 | | .

Q20:

Find the components of the vector , where and .

  • A
  • B
  • C
  • D
  • E

Q21:

What is the magnitude of the vector 𝐴 𝐵 , where 𝐴 = ( 9 . 1 , 2 . 3 ) and 𝐵 = ( 7 . 7 , 2 . 5 ) ?

Q22:

Using the shown graph, determine the position vector of point 𝐶 relative to the origin point 𝑂 , denoted by 𝑂 𝐶 , and find its norm, denoted by | | 𝑂 𝐶 | | .

  • A 𝑂 𝐶 = 9 , 6 , | | 𝑂 𝐶 | | = 3 1 3
  • B 𝑂 𝐶 = 9 , 6 , | | 𝑂 𝐶 | | = 1 5
  • C 𝑂 𝐶 = 6 , 9 , | | 𝑂 𝐶 | | = 3 1 3
  • D 𝑂 𝐶 = 9 , 6 , | | 𝑂 𝐶 | | = 3 1 3
  • E 𝑂 𝐶 = 6 , 9 , | | 𝑂 𝐶 | | = 1 5

Q23:

What is the initial point of the vector 𝑢 in the given diagram?

  • A 𝐴
  • B 𝐵

Q24:

What is the terminal point of the vector 𝑢 in the given diagram?

  • A 𝐵
  • B 𝐴

Q25:

The points 𝐴 , 𝐵 , and 𝐶 have coordinates ( 7 , 1 ) , ( 2 , 4 ) , and ( 4 , 1 ) respectively. Given that 𝐴 𝐵 and 𝐶 𝐷 are equivalent vectors, find the coordinates of 𝐷 .

  • A ( 9 , 4 )
  • B ( 2 , 1 )
  • C ( 4 , 9 )
  • D ( 1 , 2 )
  • E ( 9 , 4 )

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