Question

vectors p,q and r are such that |p|=|q| ,|r|=√2|p|, p+q+R=0 then what is the angle between p and q, q and r and p and r

Answer 1

Explanation:

When,

p + Q = R

or P−R =−Q

( P−R ).( P − R )=(− Q ).(− Q )

P2 +R 2−2PRcosθ1

=Q2

cosθ 1 =1/2 (as P=Q=R)θ1 =60°

When, P + Q+R=0 or

p +R=−Q(P+ R ).( P + R )=(− Q ).(−Q )P2+R2+2PRcosθ2 =Q2cosθ2

=−1/2 (as P=Q=R)θ2 =120.°

Thus, θ1 =θ2/2

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