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Question

The points A, B and C with position vectors 2^i+3^j+5^k,^i+2^j+3^k and 7^i^k respectively are non collinear.

A
True
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B
False
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Solution

The correct option is B False
A=2^i+3^j+5^k,^i+2^j+3^k and 7^i^kA=2^i+3^j+5^kB=^i+2^j+3^kC=7^i^kAB will be given by OBOA=(^i+2^j+3^k)(2^i+3^j+5^k)=3^i^j2^kAC=OCOA=(7^i^k)(2^i+3^j+5^k)=9^i3^j6^k=3(3^i^j2^k)AC=3AB
AC is parallel to AB with A as a common point. So A, B and C are collinear.

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