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Q. 122 If p + q +r = xs , q +r +s-yp non coplanar vectors, then p + q +-+-|- and are p,q,r (A) I (C) 2 3 (D) 31268365

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Answer #1

Given:

p + q + r = x*s -----> 1

q + r + s = y*p ------> 2 and p, q, r are not coplanar.

Eqn. 2 can be re-written as s = y*p - q - r -------> 3

Put Eqn. 3 in Eqn 1,

p + q + r = x*(y*p - q - r)

=> p( 1 - x*y ) + (1+x)* (q+r) = 0 Since, p, q, r are not coplanar => a*p + b*q + c*r = 0 only if a,b,c each is Zero. Making p,q,r independent vectors.

=> 1 + x = 0 and 1 - x*y = 0

=> x = -1 and 1 - (-1)*y = 0 => y = -1.

Substitute x in Eqn. 1 to get p + q + r + s = 0

As the vector itself is zero vector => it's magnitude i.e: |p + q + r + s| = 0

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