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Lesson: Products of Vectors

Video

12:52

Sample Question Videos

Worksheet • 14 Questions • 1 Video

Q1:

Calculate the product .

  • A
  • B
  • C
  • D
  • E

Q2:

For the vectors shown in the accompanying diagram, the positive -axis corresponds to horizontally right and the positive -axis corresponds to vertically upward.

Find the component of vector along vector .

Find the component of vector along vector .

Find the component of vector along vector .

Find the component of vector along vector .

Q3:

Consider the vectors .

Find .

  • A
  • B
  • C
  • D
  • E

Find .

Find the angle between and .

Find the angle between and .

Q4:

A convoy of vehicles has a velocity vector .

What is the unit vector of the convoy’s direction of motion?

  • A
  • B
  • C
  • D
  • E

At what angle north of east does the convoy move?

Q5:

The positive π‘₯ -axis is horizontal to the right for the vectors shown.

What is the vector product ⃑ 𝐴 Γ— ⃑ 𝐢 ?

  • A βˆ’ 1 2 0 ⃑ π‘˜
  • B βˆ’ 1 1 6 ⃑ π‘˜
  • C βˆ’ 1 2 5 ⃑ π‘˜
  • D βˆ’ 1 1 7 ⃑ π‘˜
  • E 1 2 0 ⃑ π‘˜

What is the vector product ⃑ 𝐴 Γ— ⃑ 𝐹 ?

  • A βˆ’ 1 7 3 ⃑ π‘˜
  • B βˆ’ 1 7 5 ⃑ π‘˜
  • C βˆ’ 1 8 5 ⃑ π‘˜
  • D 1 7 7 ⃑ π‘˜
  • E βˆ’ 1 8 0 ⃑ π‘˜

What is the vector product ⃑ 𝐷 Γ— ⃑ 𝐢 ?

  • A 9 3 . 7 ⃑ π‘˜
  • B βˆ’ 1 7 5 ⃑ π‘˜
  • C βˆ’ 1 8 5 ⃑ π‘˜
  • D 1 7 7 ⃑ π‘˜
  • E βˆ’ 1 8 0 ⃑ π‘˜

What is the vector product ⃑ 𝐴 Γ— ( ⃑ 𝐹 + 2 ⃑ 𝐢 ) ?

  • A βˆ’ 4 1 3 ⃑ π‘˜
  • B 4 1 6 ⃑ π‘˜
  • C 4 0 3 ⃑ π‘˜
  • D βˆ’ 4 2 1 ⃑ π‘˜
  • E βˆ’ 4 0 8 ⃑ π‘˜

What is the vector product ⃑ 𝑖 Γ— ⃑ 𝐡 ?

  • A 4 0 ⃑ π‘˜
  • B βˆ’ 4 2 ⃑ π‘˜
  • C 4 4 ⃑ π‘˜
  • D βˆ’ 3 9 ⃑ π‘˜
  • E 3 7 ⃑ π‘˜

What is the vector product ⃑ 𝑗 Γ— ⃑ 𝐡 ?

  • A βˆ’ 1 2 0 ⃑ π‘˜
  • B 1 1 0 ⃑ π‘˜
  • C βˆ’ 9 0 ⃑ π‘˜
  • D 9 3 ⃑ π‘˜
  • E βˆ’ 1 0 0 ⃑ π‘˜

What is the vector product ( 3 ⃑ 𝑖 βˆ’ ⃑ 𝑗 ) Γ— ⃑ 𝐡 ?

  • A 1 5 0 ⃑ π‘˜
  • B βˆ’ 1 1 0 ⃑ π‘˜
  • C βˆ’ 1 6 0 ⃑ π‘˜
  • D βˆ’ 1 3 0 ⃑ π‘˜
  • E 1 4 0 ⃑ π‘˜

Q6:

Calculate the product .

  • A
  • B
  • C
  • D
  • E

Q7:

Three dogs pull on a stick, all in different directions, exerting forces , , and . N, N, and N. The forces , , and apply the displacement vector cm to the stick.

What is the angle between and ?

What magnitude of work is done by ?

What magnitude of work is done by ?

Q8:

Calculate the product .

Q9:

Calculate the product .

Q10:

Find the angle between the two vectors and .

Q11:

What is the relationship between the directions of two vectors for which the dot product is zero?

  • AThey are perpendicular (orthogonal).
  • BThey are antiparallel.
  • CThey are parallel.
  • DThey form a 45 degrees angle with respect to one another.
  • EThey are coplanar.

Q12:

Calculate the dot product of and . Which of the following matches the result?

  • A44
  • B38
  • C12
  • D72
  • E16

Q13:

Calculate the cross product of and . Which of the following best matches the result?

  • A
  • B
  • C
  • D
  • E

Q14:

Find the angle between the two vectors ⃑ 𝑦 = ( 2 ⃑ 𝑖 + 4 ⃑ 𝑗 + 8 ⃑ π‘˜ ) and ⃑ 𝑧 = ( 6 ⃑ 𝑖 + 4 ⃑ 𝑗 + 2 ⃑ π‘˜ ) in degrees. Which of the following best matches the result?

  • A 50 degrees
  • B 5 degrees
  • C 55 degrees
  • D 32 degrees
  • E 70 degrees
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