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Question
Let `veca = 4hati + 5hatj - hatk`, `vecb = hati - 4hatj + 5hatk` and `vecc = 3hati + hatj - hatk`. Find a vector `vecd` which is perpendicular to both `vecc` and `vecb and vecd.veca = 21`
Solution
Let `vecd = xhati + yhatj + zhatk`
Since `vecd` is perpendicular to both `vecc` and `vecb`, so
`vecd.vecc = 0` and `vecd.vecb = 0`
3x + y - z = 0 ....1
x - 4y + 5z = 0 ....2
`vecd.veca = 21`
4x + 5x - z = 21 ....3
Solving 1, 2 and 3
`x = (-1/3), y = 16/3 , z = 13/3`
`vecd = 1/3 (-hati + 16hatj + 13hatk)`
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