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प्रश्न
Let `veca = hati + hatj, vecb = hati - hatj` and `vecc = hati + hatj + hatk`. If `hatn` is a unit vector such that `veca.hatn` = 0 and `vecb.hatn` = 0, then find `|vecc.hatn|`.
उत्तर
Given, `veca = hati + hatj, vecb = hati - hatj`
and `vecc = hati + hatj + hatk`
Also, given `veca.hatn` = 0
and `vecb.hatn` = 0
Here, `hatn = (veca xx vecb)/(|veca xx vecb|)`
Here, `veca xx vecb = |(hati, hatj, hatk),(1, 1, 0),(1, -1, 0)|`
= `hati(0 - 0) - hatj(0 - 0) + hatk(-1 - 1)`
= `-2hatk`
∴ `hatn = (-2hatk)/sqrt((-2)^2) = - hatk`
Therefore, `|vecc.hatn| = |(hati + hatj + hatk).(-hatk)|`
= |–1|
= 1
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