Question

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

Answer 1

ANSWER

a) Orthogonal

b) Not orthogonal.

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.

$v1 \bullet \: v2= - 5 \times 1 + 5 \times 1$

$v1 \bullet \: v2= - 5 \times 1 + 5 \times 1 = - 5 + 5$

$v1 \bullet \: v2= 0$

These two vectors are orthogonal.

b)

The second pair of vectors are:

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

and

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

$v1 \bullet \: v2= 154\times 88 + - 169.4\times 64$

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

$v1 \bullet \: v2= 2712.4$

This pair is not orthogonal.