Question

Use the dot product to determine which of the following vector pairs are orthogonal.

(a) v1=(-5, 5) and v2=(1, 1)

(b) v1=(154, -169.4) and v2=(88, 64)

Answer 1

a) Orthogonal

b) Not orthogonal.

Step-by-step explanation

The given vectors are:

a)

`v1 = \: < \: - 5,5 \: >`

and

`v2= \: < \: 1,1 \: >`

If the dot product of two vectors is zero, then the two vectors are orthogonal.

`v1 \bullet \: v2= - 5 * 1 + 5 * 1`

`v1 \bullet \: v2= - 5 * 1 + 5 * 1 = - 5 + 5`

`v1 \bullet \: v2= 0`

These two vectors are orthogonal.

b)

The second pair of vectors are:

`v1 = \: < \: 154, -169.4 \: >`

and

`v2 = \: < \: 88,64 \: >`

`v1 \bullet \: v2= 154* 88 + - 169.4* 64`

`v1 \bullet \: v2= 13552 - 10841.6`

`v1 \bullet \: v2= 2712.4`

This pair is not orthogonal.