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Lesson: Cross Product

Sample Question Videos

Worksheet • 15 Questions • 3 Videos

Q1:

Let and . Calculate .

  • A
  • B
  • C
  • D
  • E

Q2:

Given that ⃑ 𝐴 = βˆ’ 9 ⃑ 𝑖 βˆ’ ⃑ 𝑗 + 3 ⃑ π‘˜ and ⃑ 𝐡 = 3 ⃑ 𝑖 βˆ’ 2 ⃑ 𝑗 βˆ’ 7 ⃑ π‘˜ , determine ⃑ 𝐴 Γ— ⃑ 𝐡 .

  • A 1 3 ⃑ 𝑖 βˆ’ 5 4 ⃑ 𝑗 + 2 1 ⃑ π‘˜
  • B ⃑ 𝑖 βˆ’ 7 2 ⃑ 𝑗 + 1 5 ⃑ π‘˜
  • C βˆ’ 2 7 ⃑ 𝑖 βˆ’ 2 ⃑ 𝑗 βˆ’ 2 1 ⃑ π‘˜
  • D 2 1 ⃑ 𝑖 βˆ’ 5 4 ⃑ 𝑗 + 1 3 ⃑ π‘˜

Q3:

Given that ⃑ 𝐴 = ( βˆ’ 5 , βˆ’ 9 , βˆ’ 1 ) and ⃑ 𝐡 = ( 2 , βˆ’ 1 , βˆ’ 7 ) , find ⃑ 𝐴 Γ— ⃑ 𝐡 .

  • A 6 2 ⃑ 𝑖 βˆ’ 3 7 ⃑ 𝑗 + 2 3 ⃑ π‘˜
  • B 6 2 ⃑ 𝑖 + 3 7 ⃑ 𝑗 + 2 3 ⃑ π‘˜
  • C 6 4 ⃑ 𝑖 + 3 3 ⃑ 𝑗 βˆ’ 1 3 ⃑ π‘˜
  • D 2 3 ⃑ 𝑖 + 6 2 ⃑ 𝑗 βˆ’ 3 7 ⃑ π‘˜

Q4:

Given that ⃑ 𝐴 = βˆ’ 3 ⃑ 𝑖 + 3 ⃑ 𝑗 βˆ’ 5 ⃑ π‘˜ and ⃑ 𝐡 = βˆ’ ⃑ 𝑖 βˆ’ 3 ⃑ 𝑗 + 5 ⃑ π‘˜ , determine ο€Ί 4 ⃑ 𝐴  Γ— ο€Ί 2 ⃑ 𝐡  .

  • A 1 6 0 ⃑ 𝑗 + 9 6 ⃑ π‘˜
  • B 8 0 ⃑ 𝑗 + 4 8 ⃑ π‘˜
  • C βˆ’ 1 6 0 ⃑ 𝑗 βˆ’ 9 6 ⃑ π‘˜
  • D 2 4 ⃑ 𝑖 βˆ’ 7 2 ⃑ 𝑗 βˆ’ 2 0 0 ⃑ π‘˜

Q5:

If ⃑ 𝐴 = ( 4 , βˆ’ 2 , βˆ’ 9 ) and ⃑ 𝐡 = ( 4 , 3 , 4 ) , determine ⃑ 𝐴 Γ— ⃑ 𝐡 .

  • A 1 9 ⃑ 𝑖 βˆ’ 5 2 ⃑ 𝑗 + 2 0 ⃑ π‘˜
  • B βˆ’ 3 5 ⃑ 𝑖 + 2 0 ⃑ 𝑗 + 4 ⃑ π‘˜
  • C 1 6 ⃑ 𝑖 + 6 ⃑ 𝑗 βˆ’ 3 6 ⃑ π‘˜
  • D 2 0 ⃑ 𝑖 βˆ’ 5 2 ⃑ 𝑗 + 1 9 ⃑ π‘˜

Q6:

If the force ⃑ 𝐹 = π‘₯ ⃑ 𝑖 + 2 ⃑ 𝑗 is acting at the point 𝐴 ( 9 , βˆ’ 4 ) , where its moment vector about the point 𝐡 ( 8 , βˆ’ 2 ) is 8 ⃑ π‘˜ , determine the value of π‘₯ .

Q7:

Given that the forces ⃑ 𝐹 = βˆ’ ⃑ 𝑖 + π‘š ⃑ 𝑗 1 , ⃑ 𝐹 = βˆ’ 2 ⃑ 𝑖 βˆ’ 8 ⃑ 𝑗 2 , and ⃑ 𝐹 = 𝑛 ⃑ 𝑖 βˆ’ 1 2 ⃑ 𝑗 3 are three parallel forces, find the values of π‘š and 𝑛 .

  • A π‘š = βˆ’ 4 , 𝑛 = βˆ’ 3
  • B π‘š = βˆ’ 4 , 𝑛 = βˆ’ 1 3
  • C π‘š = βˆ’ 1 6 , 𝑛 = βˆ’ 1 3
  • D π‘š = βˆ’ 1 6 , 𝑛 = βˆ’ 3

Q8:

and are two vectors, where and . Calculate .

  • A
  • B
  • C
  • D
  • E

Q9:

⃑ 𝑉 and οƒŸ π‘Š are two vectors, where ⃑ 𝑉 = βˆ’ ⃑ 𝑖 + 2 ⃑ 𝑗 + ⃑ π‘˜ and οƒŸ π‘Š = βˆ’ 3 ⃑ 𝑖 + 6 ⃑ 𝑗 + 3 ⃑ π‘˜ . Calculate ⃑ 𝑉 Γ— οƒŸ π‘Š .

  • A ( 0 , 0 , 0 )
  • B ( 0 , 6 , βˆ’ 1 2 )
  • C ( 3 , 1 2 , 3 )
  • D ( 1 2 , 0 , 1 2 )
  • E ( βˆ’ 3 , 6 , 9 )

Q10:

and are two vectors, where and . Calculate .

  • A
  • B
  • C
  • D
  • E

Q11:

If ⃑ 𝐴 = ( 3 , 4 , βˆ’ 4 ) , ⃑ 𝐡 = ( 2 , 5 , βˆ’ 4 ) , and ⃑ 𝐢 = ( βˆ’ 4 , βˆ’ 4 , 2 ) , find ο€Ί ⃑ 𝐴 βˆ’ ⃑ 𝐡  Γ— ο€Ί ⃑ 𝐢 βˆ’ ⃑ 𝐴  .

  • A βˆ’ 6 ⃑ 𝑖 βˆ’ 6 ⃑ 𝑗 βˆ’ 1 5 ⃑ π‘˜
  • B βˆ’ 2 ⃑ 𝑖 βˆ’ 2 ⃑ 𝑗 βˆ’ 8 ⃑ π‘˜
  • C βˆ’ 2 ⃑ 𝑖 + 1 6 ⃑ 𝑗 + 1 9 ⃑ π‘˜
  • D 6 ⃑ 𝑖 + 6 ⃑ 𝑗 + 1 5 ⃑ π‘˜

Q12:

Find the unit vectors that are perpendicular to both ⃑ 𝐴 = ( 4 , 2 , 0 ) and ⃑ 𝐡 = ( 4 , 6 , βˆ’ 4 ) .

  • A ( βˆ’ 1 , 2 , 2 ) or ( 1 , βˆ’ 2 , βˆ’ 2 )
  • B ο€Ό βˆ’ 1 3 , 2 3 , 2 3  or ο€Ό 1 3 , βˆ’ 2 3 , βˆ’ 2 3 
  • C ( βˆ’ 2 4 , 4 8 , 4 8 ) or ( 2 4 , βˆ’ 4 8 , βˆ’ 4 8 )
  • D ( βˆ’ 8 , 1 6 , 1 6 ) or ( 8 , βˆ’ 1 6 , βˆ’ 1 6 )

Q13:

and are two vectors, where and . Calculate .

  • A
  • B
  • C
  • D
  • E

Q14:

Given that ⃑ 𝐴 = ( βˆ’ 3 , 4 , 0 ) , and ⃑ 𝐡 = ( 1 , βˆ’ 5 , 1 ) , determine the unit vector perpendicular to the plane of the two vectors ⃑ 𝐴 and ⃑ 𝐡 .

  • A 4 √ 1 4 6 ⃑ 𝑖 + 3 √ 1 4 6 ⃑ 𝑗 + 1 1 √ 1 4 6 ⃑ π‘˜
  • B 4 √ 1 4 6 ⃑ 𝑖 βˆ’ 3 √ 1 4 6 ⃑ 𝑗 + 1 1 √ 1 4 6 ⃑ π‘˜
  • C 1 1 √ 3 8 6 ⃑ 𝑖 + 4 √ 3 8 6 ⃑ 𝑗 + 3 √ 3 8 6 ⃑ π‘˜
  • D 4 √ 3 8 6 ⃑ 𝑖 βˆ’ 3 √ 3 8 6 ⃑ 𝑗 + 1 9 √ 3 8 6 ⃑ π‘˜

Q15:

Let and . Calculate .

  • A
  • B
  • C
  • D
  • E
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