Question

If either vector `veca = vec0`  or `vecb = vec0`, then `veca.vecb = 0`. But the converse need not be true. Justify your answer with an example.

Answer 1

It is given that when `veca = 0` or `vecb = 0`, then `veca xx vecb = 0`. But if `veca xx vecb = 0`, then it is not true that `veca, vecb` is zero.

Let `veca = hati - 2hatj + hatk, vecb = hati + 3hatj + 5hatk`

`|veca| = sqrt(1^2 + (-2)^2 + 1^2)`

`= sqrt(1 + 4 + 1)`

`= sqrt6`

and `|vecb| = sqrt(1^2 + 3^2 + 5^2) `

`= sqrt(1 + 9 + 25)`

`= sqrt35`

`veca xx vecb = (hati - 2hatj + hatk)(1 + 3hatj + 5hatk)`

= 1.1 - 2.3 + 1.5

= 0

Hence, `veca xx vecb = 0` thought `veca ≠ 0, vecb ≠ 0.`