Q.

If a, b¯ and c¯ are non –coplanar vectors and if d¯ is such that d¯=1x(a¯+b¯+c¯) and a¯=1y(b¯+c¯+d¯) where x and y are non zero real numbers, then 1xy(a¯+b¯+c¯+d¯)=

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a

a¯

b

0¯

c

2a¯

d

3a¯

answer is B.

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Detailed Solution

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Given xd¯=a¯+b¯+c¯d¯=a¯+b¯+c¯x(1) and  a¯y=b¯+c¯+d¯a¯y=b+c¯+a¯+b¯+c¯x a¯y-b-c-a¯+b¯+c¯x =0a¯(y-1x)-b(1+1x)-c¯(1+1x)=0since a¯,b,c are non-coplanar then y-1x=0xy=1 and1+1x=0x=-1 and y=-1now from (1) 1xy(a¯+b¯+c¯+d)=0

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