Worksheet: Dot Product in 3D

In this worksheet, we will practice finding the dot product of two vectors in 3D.

Q1:

If A and B are two perpendicular vectors, then AB=.

Q2:

If the dot product of two nonzero vectors is zero, what does this tell us about the two vectors?

  • AThe two vectors are equal in magnitude but opposite in direction.
  • BThey are parallel in opposite directions.
  • CThey are perpendicular.
  • DIt does not indicate anything about the two vectors.
  • EThey are parallel in the same direction.

Q3:

For the unit vectors i, j, k, what is ii?

Q4:

Given that A=6,3,5 and B=7,4,1, determine AB.

Q5:

Given that the coordinates of 𝐴, 𝐵, and 𝐶 are (2,4,2), (2,3,3), and (4,2,5), respectively, determine 𝐴𝐵𝐴𝐶.

Q6:

For what value of 𝑘 are vectors A=7,7𝑘,6 and B=7,3,𝑘 perpendicular?

  • A4915
  • B4915
  • C73
  • D715

Q7:

Given that Aijk=57+7 and Bijk=725, determine AB.

Q8:

If A and B are two perpendicular unit vectors, find (3)(2+)ABAB.

Q9:

Which of the following is true of the vectors A=3,7,8 and B=6,1,1?

  • AThey are perpendicular.
  • BThey are neither parallel nor perpendicular.
  • CThey are parallel.

Q10:

If A=0,3,1 and Bijk=24, find AB.

Q11:

Given that Aijk=35+, Bijk=533, Cijk=2+4, and (+𝑚)AB is perpendicular to the vector C, determine 𝑚.

Q12:

If Aijk=3+3+4𝑚, Bijk=467, and AB, find the value of 𝑚.

  • A314
  • B174
  • C1514
  • D32

Q13:

Determine 𝑚, given that the scalar product of the two vectors Aijk=𝑚66 and Bijk=2+84 is 27.

Q14:

For the unit vectors i, j, k, what is kk?

Q15:

For the unit vectors i, j, k, what is jk?

Q16:

If Aijk=253 and Bijk=42, find AB.

Q17:

If Aijk=3+23, Bijk=22, and Cijk=23, find 2[2(2+4)]CABCB.

  • A244+246+118ijk
  • B248248124ijk
  • C246+247+121ijk
  • Djk2

Q18:

For the unit vectors i, j, k, what is ki?

Q19:

Given that 5=1015+10Aijk and 4=8+124Bijk, determine 44AB.

Q20:

Suppose A=1,2,7, ||=13B, and the angle between the two vector is 135. Find AB to the nearest hundredth.

Q21:

Given that AB=2, AC=3, AD=3, B=3,2,2, C=3,3,1, and D=1,2,2, determine A.

  • A10,414,154
  • B0,0,0
  • C10,414,154
  • D414,154,10

Q22:

Given that A and B are two unit vectors, and |+|=1AB, evaluate (6+4)(2+)ABAB.

Q23:

For the unit vectors i, j, k, what is jj?

Q24:

For the unit vectors i, j, k, what is ij?

Q25:

If A and B are unit vectors, which interval does AB lie in?

  • A[1,1]
  • B(0,1)
  • C(1,1)
  • D

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