Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Components of a Vector

Video

11:44

Worksheet • 16 Questions

Q1:

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

  • A
  • B
  • C
  • D
  • E

Q2:

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 βˆ’ 1 9 0 ⃑ 𝑖 cm
  • C 1 9 0 ⃑ 𝑗 cm
  • D βˆ’ 1 9 0 ⃑ 𝑗 cm

Q3:

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

  • A
  • B
  • C
  • D
  • E

Q4:

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

  • A ( βˆ’ 3 , βˆ’ 4 )
  • B ( 3 , 4 )
  • C ( βˆ’ 4 , βˆ’ 3 )
  • D ( 3 , βˆ’ 4 )
  • E ( βˆ’ 3 , 4 )

Q5:

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

  • A
  • B
  • C
  • D
  • E

Q6:

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

  • A ( βˆ’ 2 , βˆ’ 4 )
  • B ( 2 , 4 )
  • C ( βˆ’ 4 , βˆ’ 2 )
  • D ( βˆ’ 2 , 4 )
  • E ( 2 , βˆ’ 4 )

Q7:

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

  • A
  • B
  • C
  • D
  • E

Q8:

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

Q9:

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

Q10:

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

  • A
  • B
  • C
  • D
  • E

Q11:

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

  • A
  • B
  • C
  • D
  • E

Q12:

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

Q13:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

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

What are the coordinates of its initial point?

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

What are the components of the vector?

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

Q14:

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

  • A
  • B
  • C
  • D
  • E

Q15:

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

  • A ( βˆ’ 3 , βˆ’ 2 )
  • B ( 3 , 2 )
  • C ( βˆ’ 2 , βˆ’ 3 )
  • D ( βˆ’ 3 , 2 )
  • E ( 3 , βˆ’ 2 )

Q16:

𝑂 is the origin point of a system of perpendicular Cartesian coordinates in a plane. ⃑ 𝐹 = ( βˆ’ 9 , 6 ) is acting at 𝑂 in the direction of  𝑂 𝑋 and  𝑂 π‘Œ . Find the two components of ⃑ 𝐹 in the direction of the two axes.

  • A9 units in the direction of  𝑂 𝑋 β€² , 6 units in the direction of  𝑂 π‘Œ
  • B9 units in the direction of  𝑂 𝑋 , 6 units in the direction of  𝑂 π‘Œ β€²
  • C9 units in the direction of  𝑂 π‘Œ , 6 units in the direction of  𝑂 𝑋 β€²
  • D3 units in the direction of  𝑂 𝑋 β€² , 15 units in the direction of  𝑂 π‘Œ
Preview