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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.
Solution
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.`
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