Worksheet: Linear Combination of Unit Vectors

In this worksheet, we will practice writing a vector as a linear combination of unit vectors.

Q1:

Express the vector 𝑍 = 5 2 , 1 9 using the unit vectors 𝑖 and 𝑗 .

  • A 𝑍 = 5 2 𝑖 + 1 9 𝑗
  • B 𝑍 = 1 9 𝑖 5 2 𝑗
  • C 𝑍 = 5 2 𝑖
  • D 𝑍 = 5 2 𝑖 1 9 𝑗
  • E 𝑍 = 1 9 𝑗

Q2:

The given figure shows a vector in a plane. Express this vector in terms of the unit vectors 𝑖 and 𝑗 .

  • A 2 𝑖 1 0 𝑗
  • B 2 𝑖 + 1 0 𝑗
  • C 1 0 𝑖 + 2 𝑗
  • D 2 𝑖 + 1 0 𝑗
  • E 2 𝑖 1 0 𝑗

Q3:

Express the vector 𝐿 = ( 1 0 , 1 0 ) using the unit vectors 𝑖 and 𝑗 .

  • A 𝐿 = 1 0 𝑖
  • B 𝐿 = 1 0 𝑖 + 1 0 𝑗
  • C 𝐿 = 1 0 𝑗
  • D 𝐿 = 1 0 𝑖 1 0 𝑗

Q4:

Express the vector 𝐿 = ( 9 , 1 3 ) using the unit vectors 𝑖 and 𝑗 .

  • A 𝐿 = 9 𝑖 + 1 3 𝑗
  • B 𝐿 = 1 3 𝑖 + 9 𝑗
  • C 𝐿 = 9 𝑖
  • D 𝐿 = 9 𝑖 1 3 𝑗
  • E 𝐿 = 1 3 𝑗

Q5:

The given figure shows a vector in a plane. Express this vector in terms of the unit vectors 𝑖 and 𝑗 .

  • A 1 1 𝑖 + 2 𝑗
  • B 1 1 𝑖 2 𝑗
  • C 2 𝑖 + 1 1 𝑗
  • D 1 1 𝑖 2 𝑗
  • E 1 1 𝑖 + 2 𝑗

Q6:

The given figure shows a vector in a plane. Express this vector in terms of the unit vectors 𝑖 and 𝑗 .

  • A 6 𝑖 3 𝑗
  • B 6 𝑖 + 3 𝑗
  • C 3 𝑖 6 𝑗
  • D 6 𝑖 + 3 𝑗
  • E 6 𝑖 3 𝑗

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