Worksheet: Components of a Vector

In this worksheet, we will practice finding the components of a given two-dimensional vector.

Q1:

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 2 , 6
  • C 4 , 6
  • D 4 , 2
  • E 4 , 2

Q2:

𝑂 is the origin point of a system of perpendicular Cartesian coordinates in a plane. F=9,6 is acting at 𝑂 in the direction of 𝑂𝑋 and 𝑂𝑌. Find the two components of F in the direction of the two axes.

  • A9 units in the direction of 𝑂𝑌, 6 units in the direction of 𝑂𝑋
  • B9 units in the direction of 𝑂𝑋, 6 units in the direction of 𝑂𝑌
  • C3 units in the direction of 𝑂𝑋, 15 units in the direction of 𝑂𝑌
  • D9 units in the direction of 𝑂𝑋, 6 units in the direction of 𝑂𝑌

Q3:

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

Q4:

A body moved 190 cm due east, where i and j are two unit vectors in the east and north directions, respectively. Express its displacement in terms of the two unit vectors i and j.

  • A 1 9 0 i cm
  • B 1 9 0 i cm
  • C 1 9 0 j cm
  • D 1 9 0 j cm

Q5:

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

Q6:

The components of the vector u are 1,2 as the terminal point of the vector is 1 units 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 3 , 4
  • D 3 , 4
  • E 3 , 4

Q7:

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

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

Q8:

The components of the vector u are 1,2 as the terminal point of the vector is 1 units 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 2 , 4
  • B 4 , 2
  • C 2 , 4
  • D 2 , 4
  • E 2 , 4

Q9:

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

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

Q10:

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

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

Q11:

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

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

Q12:

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

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

Q13:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

  • A ( 1 , 3 )
  • B ( 0 , 4 )
  • C ( 3 , 1 )
  • D ( 3 , 5 )
  • E ( 5 , 3 )

What are the coordinates of its initial point?

  • A ( 5 , 3 )
  • B ( 3 , 5 )
  • C ( 3 , 1 )
  • D ( 0 , 4 )
  • E ( 1 , 3 )

What are the components of the vector?

  • A 3 , 1
  • B 0 , 4
  • C 0 , 4
  • D 4 , 0
  • E 3 , 5

Q14:

Consider the vector v in the given diagram.

What are the coordinates of its terminal point?

  • A ( 2 , 2 )
  • B ( 2 , 2 )
  • C ( 6 , 0 )
  • D ( 4 , 2 )
  • E ( 4 , 2 )

What are the coordinates of its initial point?

  • A ( 2 , 2 )
  • B ( 6 , 0 )
  • C ( 2 , 2 )
  • D ( 2 , 4 )
  • E ( 4 , 2 )

What are the components of the vector?

  • A 2 , 2
  • B 6 , 0
  • C 4 , 2
  • D 6 , 0
  • E 0 , 6

Q15:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

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

What are the coordinates of its initial point?

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

What are the components of the vector?

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

Q16:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

  • A ( 7 , 1 )
  • B ( 1 , 2 )
  • C ( 2 , 1 )
  • D ( 1 , 7 )
  • E ( 6 , 3 )

What are the coordinates of its initial point?

  • A ( 2 , 1 )
  • B ( 7 , 1 )
  • C ( 1 , 7 )
  • D ( 1 , 2 )
  • E ( 6 , 3 )

What are the components of the vector?

  • A 1 , 2
  • B 6 , 3
  • C 1 , 7
  • D 3 , 6
  • E 6 , 3

Q17:

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

What are the coordinates of its terminal point?

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

What are the components of the vector?

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

Q18:

What is the name given to the vector 0,0?

  • Athe unit vector
  • Bthe zero vector
  • Cthe origin vector
  • Dthe empty vector

Q19:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

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

What are the coordinates of its initial point?

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

What are the components of the vector?

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

Q20:

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

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

Q21:

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

  • Ayes
  • Bno

Q22:

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

Q23:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

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

What are the coordinates of its initial point?

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

What are the components of the vector?

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

Q24:

Find the components of the vector 𝐴𝐵.

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

Q25:

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

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

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