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Question

If a=x^i+(x1)^j+^k and b=(x+1)^i+^j+a^k always make an acute angle with each other for every value of x ϵ R, then


A

a ϵ (,2)

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B

a ϵ (2,)

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C

a ϵ (,1)

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D

a ϵ (1,)

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Solution

The correct option is B

a ϵ (2,)


a.b=(x^i+(x1)^j+^k).((x+1)^i+^j+a^k)=x(x+1)+x1+a=x2+2x+a1
If the angle between a and b is acute
a.b>0 x ϵ Rx2+2x+a1>0 x ϵ R
The discriminant of the quadratic expression must be negative
44(a1)<0a>2


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