Worksheet: Operations on Vectors in Space

In this worksheet, we will practice how to make operations on vectors in space, such as vector addition, vector subtraction, and scalar multiplication.

Q1:

Given that A B + = 2 , 4 , 3 and A = 3 , 5 , 3 , determine | | B .

  • A 1 1 8
  • B26
  • C118
  • D 2 6

Q2:

Find the value of 𝐴 × 𝐵 + | 𝐴 𝐵 | 2 𝐴 𝐵 2 2 2 2 .

  • A2
  • B1
  • C0
  • D 1 2
  • E 1 4

Q3:

Suppose 𝐴 and 𝐵 are two vectors in 3 . Is 𝐴 + 𝐵 = 𝐴 + 𝐵 ? If not, which is greater?

  • Ayes
  • Bno, 𝐴 + 𝐵
  • Cno, 𝐴 + 𝐵

Q4:

If A i j k = 5 8 + 6 and B i j k = 4 3 + 1 3 , find A B .

  • A 9 1 1 2 0 i j k
  • B 1 1 + 1 9 i j k
  • C 1 1 4 2 0 i j k
  • D 9 5 7 i j k

Q5:

If A = 8 , 9 , 9 and B = 6 , 4 , 9 , find 2 5 4 5 A B .

  • A 8 , 2 5 , 1 8 5
  • B 8 , 2 5 , 1 8 5
  • C 8 5 , 2 5 , 1 8 5

Q6:

If A = 1 , 1 , 1 , and B = 1 , 1 , 2 , determine the vector C for which 2 + 5 = 5 C A B .

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

Q7:

and are two vectors, where and . Comparing and , which quantity is larger?

  • AThey are both the same.
  • B
  • C

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