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Q.

A vector  d→ is equally inclined to three vector a→=i^−j^+k^,b→=2i^+j^ and c→=3j^−2k^ . Let x→,y→ and z→  be three vectors in the plane of a→,b→;b→,c→;c→,a→  respectively. Then

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a

x→⋅d→=−1

b

y→⋅d→=1

c

z→⋅d→=0

d

r→⋅d→=0,  where r→=λx→+μv→+δz→

answer is C.

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Detailed Solution

Since [a→b→c→]=0,a→,b→ and c→ are coplanar vectors.Further, since  d→  is equally inclined to  a→,b→ and c→d→⋅a→=d→⋅b→=d→⋅c→=0d→⋅x→=d→⋅y→=d→⋅z→=0d→⋅r→=0
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