Q22 of 29 Page 1

Ifand, find a vector of magnitude unitsperpendicular to the vectorand coplanar with vectorsand

Letbe the required vector.


,


As, it is given thatis perpendicular to, therefore



⇒ a – 2b + c = 0 … (1)


Also,andare coplanar, therfore



⇒ 1(-2c - b) - 1(c - a) + 1(b - ( -2a)) = 0


⇒ -2c - b - c + a + b + 2a = 0


⇒ 2a + a – b + b – 2c – c = 0


⇒ 3a – 3c = 0


⇒ a – c = 0 … (2)


Solving (1) and (2) we get,




⇒ a = b = c





So, a = 5


Hence


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