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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

ConceptProduct of Two Vectors Vector (Or Cross) Product of Two Vectors

#### 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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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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