Question

Determine whether a and b are orthogonal, parallel or neither.

i. vector a = - 3/5 i + 1/2 j + 1/3 k, b = 5i + 4j + 3k

ii. vector a = 4i - j + 6k, b = 5i - 2j + 4k

Answer 1

i. vector a = - 3/5 i + 1/2 j + 1/3 k, b = 5i + 4j + 3k

= -3 + 2 + 1 

= 0

Since, \(\overline{a}, \overline{b}\) are non-zero vectors and \(\overline{a} . \overline{b} = 0\) \(\overline{a}\) is orthogonal to \(\overline{b}.\)

ii. vector a = 4i - j + 6k, b = 5i - 2j + 4k

∴ \(\overline{a}\) is not orthogonal to \(\overline{b}.\)

It is clear that \(\overline{a}\) is not a scalar multiple of \(\overline{b}.\)

∴ \(\overline{a}\) is not parallel to \(\overline{b}.\)

Hence, \(\overline{a}\) is neither parallel nor orthogonal to \(\overline{b}.\)