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Worksheet: Products of Vectors

Q1:

Calculate the product C F × .

  • A 1 1 5 k
  • B 1 4 4 k
  • C 1 8 0 k
  • D 1 5 8 k
  • E 1 0 8 k

Q2:

Calculate the product F C .

Q3:

Find the angle between the two vectors y i j k = ( 2 . 0 + 4 . 0 + 8 . 0 ) and z i j k = ( 6 . 0 + 4 . 0 + 6 . 0 ) .

Q4:

Calculate the cross product of y i j k = ( 2 + 4 + 8 ) and z i j k = ( 6 + 4 + 2 ) . Which of the following best matches the result?

  • A ( 8 + 4 8 + 8 ) i j k
  • B ( 2 8 + 1 2 + 8 ) i j k
  • C ( 3 2 4 2 4 ) i j k
  • D ( 2 4 + 4 4 1 6 ) i j k
  • E ( 2 1 2 + 8 ) i j k

Q5:

Calculate the dot product of y i j k = ( 2 + 4 + 8 ) and z i j k = ( 6 + 4 + 2 ) . Which of the following matches the result?

  • A16
  • B12
  • C72
  • D44
  • E38

Q6:

Consider the vectors A i j = and B i j = 3 .

Find A B × .

  • A 3 k
  • B k
  • C 2 k
  • D 2 k
  • E 3 k

Find | × | A B .

Find the angle between A and B .

Find the angle between ( × ) A B and C i k = + .

Q7:

A convoy of vehicles has a velocity vector v i j = ( 4 . 0 + 3 . 0 ) / k m h .

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

  • A 0 . 6 + 0 . 9 i j
  • B 4 . 0 + 3 . 0 i j
  • C 1 . 8 + 2 . 3 i j
  • D 0 . 8 + 0 . 6 i j
  • E 2 . 0 + 1 . 5 i j

At what angle north of east does the convoy move?

Q8:

Three dogs pull on a stick, all in different directions, exerting forces F 1 , F 2 , and F 3 . F i j k 1 = ( 1 0 . 0 2 0 . 4 + 2 . 0 ) N, F i k 2 = ( 1 5 . 0 6 . 2 ) N, and F i j 3 = ( 5 . 0 + 1 2 . 5 ) N. The forces F 1 , F 2 , and F 3 apply the displacement vector D j k = ( 7 . 9 4 . 2 ) cm to the stick.

What is the angle between F 1 and F 3 ?

What magnitude of work is done by F 1 ?

What magnitude of work is done by F 2 ?

Q9:

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

Find the component of vector A along vector C .

Find the component of vector C along vector A .

Find the component of vector i along vector F .

Find the component of vector F along vector i .

Q10:

Calculate the product A B .

Q11:

The positive 𝑥 -axis is horizontal to the right for the vectors shown.

What is the vector product A C × ?

  • A 1 2 0 k
  • B 1 2 5 k
  • C 1 1 7 k
  • D 1 2 0 k
  • E 1 1 6 k

What is the vector product A F × ?

  • A 1 7 3 k
  • B 1 7 7 k
  • C 1 8 0 k
  • D 1 8 5 k
  • E 1 7 5 k

What is the vector product D C × ?

  • A 1 7 5 k
  • B 1 8 5 k
  • C 9 3 . 7 k
  • D 1 8 0 k
  • E 1 7 7 k

What is the vector product A F C × ( + 2 ) ?

  • A 4 1 3 k
  • B 4 1 6 k
  • C 4 2 1 k
  • D 4 0 3 k
  • E 4 0 8 k

What is the vector product i B × ?

  • A 3 9 k
  • B 3 7 k
  • C 4 4 k
  • D 4 0 k
  • E 4 2 k

What is the vector product j B × ?

  • A 1 0 0 k
  • B 1 1 0 k
  • C 9 0 k
  • D 1 2 0 k
  • E 9 3 k

What is the vector product ( 3 ) × i j B ?

  • A 1 1 0 k
  • B 1 5 0 k
  • C 1 6 0 k
  • D 1 3 0 k
  • E 1 4 0 k

Q12:

Calculate the product A B × .

  • A 2 4 . 2 k
  • B 4 4 . 0 k
  • C 2 8 . 8 k
  • D 4 0 . 0 k
  • E 3 4 . 0 k

Q13:

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

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

Q14:

Which of the following is closest to the angle between the two vectors y i j k = ( 2 + 4 + 8 ) and z i j k = ( 6 + 4 + 2 ) ?

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