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Question

The vectors a=x^i+(x+1)^j+(x+2)^k,b=(x+3)^i+(x+4)^j+(x+5)^k and c=(x+6)^i+(x+7)^j+(x+8)^k are coplanar for

A
all values of x
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B
x < 0
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C
x > 0
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D
None of these
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Solution

The correct option is A all values of x
a,b,c are coplanar, iff [a b c]=0
We have, [a b c]=∣ ∣xx+1x+2x+3x+4x+5x+6x+7x+8∣ ∣
=∣ ∣xx+1x+2333666∣ ∣[Applying R2 R2 R1,R3 R3 R1]
= 0 for all x [R1 and R2 are proportional]

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