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Question

Let b and c are non-collinear vectors. If a is a vector such that a.(b+c)=4 and a×(b×c)=(x22x+6)b+(sin y)c, then (x, y) lies on the line

A
x + y = 0
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B
x - y = 0
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C
x = 1
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D
y=π
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Solution

The correct option is C x = 1
a×(b×c)=(x22x+6)b+(sin y)c(a.c)b(a.b)c=(x22x+6)b+(sin y)ca.c=x22x+6,a.b=sin y
Given, a.(b+c)=4sin y+x22x+6=4x22x+2=sin y(x1)2+1=sin y x=1 and siny=1
(x,y) lies on the line x =1

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