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Question

The value of c so that for all real x, then vectors cx^i6^j+3^k,x^i+2^j+2cx^k make an obtuse angle are-

A
c<0
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B
0<c<4/3
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C
4/3<c<0
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D
c>0
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Solution

The correct option is A c<0
¯a=cx^i6^j+3^k
¯b=x^i+2^j+2cx^k

¯a & ¯b contain an obtuse angle
cosθ=¯a.¯b|¯a|¯b<0
(cx212+6cx)c2x2+36+9x2+4+4c2x2<0
cx2+6cx12<0
c(x2+6x)<12
c<12x2+6x=12x2+6x+99 =12(x+3)29
c<min[12(x+3)29]
c<129
c<0

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