Worksheet: Inner Products of Vectors

In this worksheet, we will practice performing inner product in Rⁿ and using it to find the magnitude of a vector, angle, or distance between two vectors.

Q1:

Given that u=1,2,3,2 and v=2,1,2,1, find the distance between u and v.

  • A52
  • B22
  • C25
  • D32
  • E27

Q2:

Given that v=1,1,1,1, find ||v.

Q3:

Given that uv,𝑅 are orthogonal vectors, complete the following comparison statement: |+|||+||uvuv.

  • A=
  • B
  • C<
  • D
  • E>

Q4:

Given v=(1,2,1,0) and u=(3,2,4,8), find ,uv.

Q5:

Given that xy,𝑅, complete the following comparison statement: |,|||×||xyxy.

  • A=
  • B
  • C
  • D>
  • E<

Q6:

Given v𝑅, complete the following comparison statement: ,0vv.

  • A<
  • B
  • C
  • D=
  • E>

Q7:

Given that u=4,1,2,2 and v=0,4,3,1, are u and v orthogonal?

  • AYes
  • BNo

Q8:

Given that uv,𝑅, where u=2,1,4,3, v=2,0,1,3, find the angle between the vectors u and v in degrees, rounded to the nearest 3 decimal places.

Q9:

True or False: ,=0vv only if v is the zero vector.

  • ATrue
  • BFalse

Q10:

Given that uvR, and that ,=𝑐|+|||uvuvuv, find the value of 𝑐.

  • A1
  • B2
  • C12
  • D4
  • E14

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