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Q.

Given three non-zero, non-coplanar vectors a→,b→ and c→⋅    r→1=pa→+qb→+c→ and r→2=a→+pb→+qc→ lf the vectors r1→+2r2→ and 2r→1+r2→  are collinear, then (p, q) is

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a

(0, 0)

b

(1, -1)

c

(-1, 1)

d

(1, 1)

answer is D.

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Detailed Solution

r1→+2r→2=(pa→+qb→+c→)+2(a→+pb→+qc→)              =(p+2)a→+(q+2p)b→+(1+2q)c→2r1→+r→2=(2p+1)a→+(2q+p)b→+(2+q)c→p+22p+1=q+2p2q+p=1+2q2+q            =p+q+2p+2q+3p+q+2p+2q+3=1⇒ p=1 and q=1
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