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

Lesson: Operations on Vectors in Space

Worksheet • 8 Questions

Q1:

Given that ⃑ 𝐴 + ⃑ 𝐡 = ( βˆ’ 2 , 4 , 3 ) and ⃑ 𝐴 = ( 3 , 5 , 3 ) , determine β€– β€– ⃑ 𝐡 β€– β€– .

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

Q2:

Find the value of β€– β€– ⃑ 𝐴 Γ— ⃑ 𝐡 β€– β€– + | ⃑ 𝐴 β‹… ⃑ 𝐡 | 2 β€– β€– ⃑ 𝐴 β€– β€– β€– β€– ⃑ 𝐡 β€– β€– 2 2 2 2 .

  • A 1 2
  • B 1 4
  • C1
  • D0
  • E2

Q3:

Suppose ⃑ 𝐴 and ⃑ 𝐡 are two vectors in ℝ 3 . Is β€– β€– ⃑ 𝐴 + ⃑ 𝐡 β€– β€– = β€– β€– ⃑ 𝐴 β€– β€– + β€– β€– ⃑ 𝐡 β€– β€– ? If not, which is greater?

  • Ano, β€– β€– ⃑ 𝐴 + ⃑ 𝐡 β€– β€–
  • Bno, β€– β€– ⃑ 𝐴 β€– β€– + β€– β€– ⃑ 𝐡 β€– β€–
  • Cyes

Q4:

If ⃑ 𝐴 = βˆ’ 5 ⃑ 𝑖 βˆ’ 8 ⃑ 𝑗 + 6 ⃑ π‘˜ and ⃑ 𝐡 = 4 ⃑ 𝑖 βˆ’ 3 ⃑ 𝑗 + 1 3 ⃑ π‘˜ , find ⃑ 𝐴 βˆ’ ⃑ 𝐡 .

  • A βˆ’ 9 ⃑ 𝑖 βˆ’ 5 ⃑ 𝑗 βˆ’ 7 ⃑ π‘˜
  • B βˆ’ ⃑ 𝑖 βˆ’ 1 1 ⃑ 𝑗 + 1 9 ⃑ π‘˜
  • C βˆ’ 1 1 ⃑ 𝑖 βˆ’ 4 ⃑ 𝑗 βˆ’ 2 0 ⃑ π‘˜
  • D βˆ’ 9 ⃑ 𝑖 βˆ’ 1 1 ⃑ 𝑗 βˆ’ 2 0 ⃑ π‘˜

Q5:

If ⃑ 𝐴 = ( βˆ’ 8 , 9 , 9 ) and ⃑ 𝐡 = ( βˆ’ 6 , 4 , 9 ) , find 2 5 ⃑ 𝐴 βˆ’ 4 5 ⃑ 𝐡 .

  • A ο€Ό 8 , 2 5 , βˆ’ 1 8 5 
  • B ο€Ό 8 5 , 2 5 , βˆ’ 1 8 5 
  • C ο€Ό βˆ’ 8 , 2 5 , βˆ’ 1 8 5 

Q6:

If ⃑ 𝐴 = ( βˆ’ 1 , 1 , 1 ) , and ⃑ 𝐡 = ( 1 , 1 , βˆ’ 2 ) , determine the vector ⃑ 𝐢 for which 2 ⃑ 𝐢 + 5 ⃑ 𝐴 = 5 ⃑ 𝐡 .

  • A ο€Ό 5 , 0 , βˆ’ 1 5 2 
  • B ( 1 0 , 0 , βˆ’ 1 5 )
  • C ο€Ό 3 , 2 , βˆ’ 1 1 2 
  • D ο€Ό 0 , 5 , βˆ’ 5 2 

Q7:

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

  • A
  • B
  • CThey are both the same.
Preview