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Lesson: Vector Operations

Sample Question Videos

Worksheet • 25 Questions • 1 Video

Q1:

Given that ⃑ 𝐴 = ( 0 , 1 ) and ⃑ 𝐡 = ( βˆ’ 3 , βˆ’ 6 ) , find 3 2 ο€Ί ⃑ 𝐴 βˆ’ ⃑ 𝐡  .

  • A ο€Ό 9 2 , 2 1 2 
  • B ο€Ό βˆ’ 9 2 , βˆ’ 1 5 2 
  • C ο€Ό βˆ’ 9 2 , 2 1 2 
  • D ο€Ό 9 2 , βˆ’ 1 5 2 

Q2:

Given that ⃑ 𝐴 = ( 0 , βˆ’ 1 ) and β€– β€– π‘˜ ⃑ 𝐴 β€– β€– = 1 2 , find the possible values of π‘˜ .

  • A 1 2 , βˆ’ 1 2
  • B12
  • C 1 1 2
  • D 1 1 2 , βˆ’ 1 1 2

Q3:

Given that ⃑ 𝐴 = ( 2 , βˆ’ 4 ) and ⃑ 𝐡 = ( βˆ’ 7 , βˆ’ 6 ) , find ⃑ 𝐴 βˆ’ 4 ⃑ 𝐡 .

  • A ( 3 0 , 2 0 )
  • B ( βˆ’ 2 6 , βˆ’ 2 8 )
  • C ( 3 0 , βˆ’ 2 8 )
  • D ( βˆ’ 2 6 , 2 0 )

Q4:

A force of newtons is being applied to an object. What other force should be applied to achieve a total force of newtons?

  • A newtons
  • B newtons
  • C newtons
  • D newtons
  • E newtons

Q5:

Given that u = ⟨ 0 , 4 ⟩ and v = ⟨ 0 , βˆ’ 5 ⟩ , find the components of u v + .

  • A ⟨ 0 , βˆ’ 1 ⟩
  • B ⟨ 0 , 1 ⟩
  • C ⟨ 0 , 9 ⟩
  • D ⟨ βˆ’ 5 , 4 ⟩
  • E ⟨ 0 , βˆ’ 2 0 ⟩

Q6:

Given that u = ⟨ 2 , βˆ’ 3 ⟩ , v = ⟨ βˆ’ 5 , 4 ⟩ , and w = ⟨ 3 , βˆ’ 1 ⟩ , find the components of u v w + + .

  • A ⟨ 0 , 0 ⟩
  • B ⟨ 0 , βˆ’ 2 ⟩
  • C ⟨ βˆ’ 3 , 1 ⟩
  • D ⟨ 4 , βˆ’ 6 ⟩
  • E ⟨ βˆ’ 1 5 , 1 2 ⟩

Q7:

Given that u = ⟨ 2 , βˆ’ 3 ⟩ , v = ⟨ 3 , 2 ⟩ , and w = ⟨ βˆ’ 1 , βˆ’ 5 ⟩ , find the components of u v w + + .

  • A ⟨ 4 , βˆ’ 6 ⟩
  • B ⟨ βˆ’ 6 , 4 ⟩
  • C ⟨ 5 , βˆ’ 1 ⟩
  • D ⟨ 0 , 0 ⟩
  • E ⟨ βˆ’ 6 , 3 0 ⟩

Q8:

Given that u = ⟨ 2 , βˆ’ 4 ⟩ and v = ⟨ 0 , 0 ⟩ , find the components of u v + .

  • A ⟨ 2 , βˆ’ 4 ⟩
  • B ⟨ 4 , βˆ’ 2 ⟩
  • C ⟨ 0 , 0 ⟩
  • D ⟨ βˆ’ 4 , 2 ⟩
  • E ⟨ βˆ’ 2 , 4 ⟩

Q9:

Shown on the grid of unit squares are the vectors u , v , and u v + .

What are the components of u ?

  • A ⟨ 4 , 1 ⟩
  • B ⟨ 5 , 2 ⟩
  • C ⟨ 4 , βˆ’ 1 ⟩
  • D ⟨ 5 , 1 ⟩
  • E ⟨ 4 , 2 ⟩

What are the components of v ?

  • A ⟨ βˆ’ 5 , 1 ⟩
  • B ⟨ 6 , 1 ⟩
  • C ⟨ 5 , 1 ⟩
  • D ⟨ βˆ’ 6 , 1 ⟩
  • E ⟨ βˆ’ 5 , 2 ⟩

What are the components of u v + ?

  • A ⟨ βˆ’ 1 , 2 ⟩
  • B ⟨ βˆ’ 2 , 3 ⟩
  • C ⟨ 1 , 2 ⟩
  • D ⟨ 1 , 3 ⟩
  • E ⟨ βˆ’ 1 , 3 ⟩

Q10:

The figure shows a regular hexagon 𝐴 𝐡 𝐢 𝐷 𝐸 𝐹 divided into 6 equilateral triangles. Which of the following is equal to οƒͺ 𝐡 𝐸 +  𝐹 𝐴 ?

  • A  𝐢 𝐷
  • B  𝐹 𝐷
  • C  𝐷 𝐢
  • D οƒͺ 𝐸 𝐹
  • E  𝐡 𝐴

Q11:

Given that u = ⟨ 2 , βˆ’ 4 ⟩ and v = ⟨ βˆ’ 2 , 4 ⟩ , find the components of u v + .

  • A ⟨ 0 , 0 ⟩
  • B ⟨ βˆ’ 4 , βˆ’ 1 6 ⟩
  • C ⟨ βˆ’ 4 , βˆ’ 8 ⟩
  • D ⟨ 0 , βˆ’ 8 ⟩
  • E ⟨ 4 , 8 ⟩

Q12:

Given that u = ⟨ βˆ’ 3 , βˆ’ 1 ⟩ , and v = ⟨ βˆ’ 2 , 5 ⟩ , find the components of u v + .

  • A ⟨ βˆ’ 5 , 4 ⟩
  • B ⟨ 2 , βˆ’ 3 ⟩
  • C ⟨ 6 , βˆ’ 5 ⟩
  • D ⟨ 1 , 6 ⟩
  • E ⟨ βˆ’ 1 , βˆ’ 6 ⟩

Q13:

Given that u = ⟨ 3 , 1 ⟩ and v = ⟨ 2 , 5 ⟩ find the components of u + v .

  • A ⟨ 5 , 6 ⟩
  • B ⟨ βˆ’ 1 , 4 ⟩
  • C ⟨ 6 , 5 ⟩
  • D ⟨ 1 , βˆ’ 4 ⟩
  • E ⟨ 8 , 3 ⟩

Q14:

and Find .

Q15:

On a lattice, where οƒ  𝐴 𝐢 = ( βˆ’ 5 , βˆ’ 5 ) , οƒŸ 𝐡 𝐢 = ( βˆ’ 1 2 , 6 ) , and 3 ⃑ 𝐢 + οƒ  𝐴 𝐡 = ( βˆ’ 8 , 1 3 ) , determine the coordinates of the point 𝐡 .

  • A ( 7 , 2 )
  • B ( βˆ’ 1 0 , 3 )
  • C ( βˆ’ 1 , 6 )
  • D ( βˆ’ 1 7 , 1 4 )

Q16:

On a lattice, where οƒ  𝐴 𝐢 = ( 3 , 3 ) , οƒŸ 𝐡 𝐢 = ( 1 3 , βˆ’ 7 ) , and 2 ⃑ 𝐢 + 2 οƒ  𝐴 𝐡 = ( βˆ’ 4 , βˆ’ 4 ) , find the coordinates of the point 𝐢 .

  • A ( 8 , βˆ’ 1 2 )
  • B ( 1 6 , βˆ’ 2 4 )
  • C ( βˆ’ 1 2 , 8 )
  • D ( 1 4 , βˆ’ 6 )
  • E ( βˆ’ 1 8 , 2 )

Q17:

Given that ⃑ 𝐴 = ( βˆ’ 4 , βˆ’ 1 ) and ⃑ 𝐡 = ( βˆ’ 2 , βˆ’ 1 ) , express ⃑ 𝐢 = ( βˆ’ 8 , βˆ’ 1 ) in terms of ⃑ 𝐴 and ⃑ 𝐡 .

  • A 3 ⃑ 𝐴 βˆ’ 2 ⃑ 𝐡
  • B βˆ’ ⃑ 𝐴 + 6 ⃑ 𝐡
  • C 5 ⃑ 𝐴 βˆ’ 6 ⃑ 𝐡
  • D 7 ⃑ 𝐴 + 1 0 ⃑ 𝐡

Q18:

If ⃑ 𝐴 = ( 1 , 2 , 1 ) , ⃑ 𝐡 = ( βˆ’ 1 , βˆ’ 1 , 0 ) , and ⃑ 𝐢 = ( βˆ’ 2 , βˆ’ 1 , 1 ) , express ⃑ 𝐢 in terms of ⃑ 𝐴 and ⃑ 𝐡 .

  • A ⃑ 𝐢 = ⃑ 𝐴 + 3 ⃑ 𝐡
  • B ⃑ 𝐢 = 3 ⃑ 𝐴 + ⃑ 𝐡
  • C ⃑ 𝐢 = ⃑ 𝐴 + ⃑ 𝐡
  • D ⃑ 𝐢 = βˆ’ 2 ⃑ 𝐴 βˆ’ ⃑ 𝐡

Q19:

When is it true that u v v u + = + ?

  • Afor any vectors u and v
  • Bonly when u and v are not perpendicular
  • Conly when u and v are equivalent
  • Donly when u and v are perpendicular
  • Eonly when u and v are parallel

Q20:

When is it true that β€– + β€– = β€– β€– + β€– β€– u v u v ?

  • Awhen u and v are parallel vectors
  • Bwhen u and v are perpendicular vectors
  • Calways
  • Dwhen u and v are equivalent vectors
  • Enever

Q21:

⃑ 𝑉 and οƒŸ π‘Š are two vectors, where ⃑ 𝑉 = ( βˆ’ 1 , 5 , βˆ’ 2 ) and οƒŸ π‘Š = ( 3 , 1 , 1 ) . Comparing β€– β€– ⃑ 𝑉 + οƒŸ π‘Š β€– β€– and β€– β€– ⃑ 𝑉 β€– β€– + β€– β€– οƒŸ π‘Š β€– β€– , which quantity is larger?

  • A β€– β€– ⃑ 𝑉 + οƒŸ π‘Š β€– β€–
  • B β€– β€– ⃑ 𝑉 β€– β€– + β€– β€– οƒŸ π‘Š β€– β€–
  • CThey are both the same.

Q22:

Find all the possible values of π‘š given ⃑ 𝐴 = ( βˆ’ 4 , 3 , 1 ) , ⃑ 𝐡 = ( 6 , βˆ’ 6 , π‘š βˆ’ 1 3 ) and β€– β€– ⃑ 𝐴 + ⃑ 𝐡 β€– β€– = 7 .

  • A18, 6
  • B1
  • C βˆ’ 1 8 , βˆ’ 6
  • D βˆ’ 5

Q23:

Given that ⃑ 𝐴 = ( 3 , 3 ) and ⃑ 𝐡 = ( 4 , 6 ) , find 1 2 ο€Ί ⃑ 𝐴 + ⃑ 𝐡  .

  • A ο€Ό 7 2 , 9 2 
  • B ο€Ό βˆ’ 1 2 , βˆ’ 3 2 
  • C ο€Ό βˆ’ 1 2 , 9 2 
  • D ο€Ό 7 2 , βˆ’ 3 2 

Q24:

Given that ⃑ 𝐴 = ( βˆ’ 9 , 4 ) and ⃑ 𝐡 = ( 3 , βˆ’ 2 ) , find βˆ’ 1 2 ο€Ί ⃑ 𝐴 + ⃑ 𝐡  .

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

Q25:

Given that ⃑ 𝐴 = ( βˆ’ 7 , 6 ) and ⃑ 𝐡 = ( 9 , βˆ’ 7 ) , find 3 2 ο€Ί ⃑ 𝐴 βˆ’ ⃑ 𝐡  .

  • A ο€Ό βˆ’ 2 4 , 3 9 2 
  • B ο€Ό 3 , βˆ’ 3 2 
  • C ο€Ό 3 , 3 9 2 
  • D ο€Ό βˆ’ 2 4 , βˆ’ 3 2 
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