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Question

Let a, b, c be distinct non - negative numbers. If the vectors a^i+a^j+c^k,^i+^k and c^i+c^j+b^k, are coplanar then c is

A
AM of a and b
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B
GM of a and b
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C
HM of a and b
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D
None of the above
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Solution

The correct option is B GM of a and b
Since, the vectors a^i+a^j+c^k,^i+^k and c^i+c^j+b^k are coplanar, therefore
∣ ∣aac101ccb∣ ∣=0
acab+ac+c2=0
c2=ab
c is the GM of a and b.

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