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Let `Veca = 4hati + 5hatj - Hatk`, `Vecb = Hati - 4hatj + 5hatk` and `Vecc = 3hati + Hatj - Hatk`. Find a Vector `Hatd` Which is Perpendicular to Both `Vecc` and `Vecb and Vecd.Veca = 21` - CBSE (Science) Class 12 - Mathematics

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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)`

  Is there an error in this question or solution?
Solution Let `Veca = 4hati + 5hatj - Hatk`, `Vecb = Hati - 4hatj + 5hatk` and `Vecc = 3hati + Hatj - Hatk`. Find a Vector `Hatd` Which is Perpendicular to Both `Vecc` and `Vecb and Vecd.Veca = 21` Concept: Product of Two Vectors - Vector (Or Cross) Product of Two Vectors.
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