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?

  • A4,2
  • B4,2
  • C2,4
  • D4,6
  • E2,6

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.

  • A3 units in the direction of 𝑂𝑋, 15 units in the direction of 𝑂𝑌
  • B9 units in the direction of 𝑂𝑋, 6 units in the direction of 𝑂𝑌
  • C9 units in the direction of 𝑂𝑌, 6 units in the direction of 𝑂𝑋
  • 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?

  • A5,3
  • B5,3
  • C5,3
  • D3,5
  • E5,3

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.

  • A190i cm
  • B190j cm
  • C190j cm
  • D190i 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?

  • A1,3
  • B1,3
  • C3,1
  • D1,3
  • E3,1

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?

  • A3,4
  • B3,4
  • C3,4
  • D3,4
  • E4,3

Q7:

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

  • A4,1
  • B4,1
  • C4,1
  • D4,1
  • E1,4

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?

  • A2,4
  • B2,4
  • C2,4
  • D2,4
  • E4,2

Q9:

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

  • A2,0
  • B0,2
  • C0,2
  • D2,0
  • E1,2

Q10:

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

  • A4,1
  • B0,4
  • C0,4
  • D4,0
  • E4,0

Q11:

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

  • A3,5
  • B3,5
  • C5,3
  • D3,5
  • E5,3

Q12:

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

  • A3,2
  • B3,2
  • C3,2
  • D3,2
  • E2,3

Q13:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

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

What are the coordinates of its initial point?

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

What are the components of the vector?

  • A3,1
  • B3,5
  • C0,4
  • D0,4
  • E4,0

Q14:

Consider the vector v in the given diagram.

What are the coordinates of its terminal point?

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

What are the coordinates of its initial point?

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

What are the components of the vector?

  • A6,0
  • B6,0
  • C2,2
  • D0,6
  • E4,2

Q15:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

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

What are the coordinates of its initial point?

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

What are the components of the vector?

  • A1,2
  • B0,3
  • C3,0
  • D3,0
  • E2,2

Q16:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

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

What are the coordinates of its initial point?

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

What are the components of the vector?

  • A3,6
  • B1,7
  • C1,2
  • D6,3
  • E6,3

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

What are the components of the vector?

  • A2,1
  • B2,1
  • C1,2
  • D2,1
  • E1,2

Q18:

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

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

Q19:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

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

What are the coordinates of its initial point?

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

What are the components of the vector?

  • A2,1
  • B3,0
  • C0,3
  • D2,2
  • E0,3

Q20:

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

  • A0,3
  • B3,3
  • C3,0
  • D3,0
  • E0,3

Q21:

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

  • Ano
  • Byes

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?

  • A1,3
  • B2,1
  • C3,1
  • D1,2
  • E2,3

Q23:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

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

What are the coordinates of its initial point?

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

What are the components of the vector?

  • A3,5
  • B4,3
  • C4,5
  • D3,4
  • E3,4

Q24:

Find the components of the vector 𝐴𝐵.

  • A5,5.1
  • B2.1,2.2
  • C2.2,5.1
  • D5,2.1
  • E2.2,2.1

Q25:

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

  • A4,6
  • B4,2
  • C2,1
  • D1,2
  • E2,4

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