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Question

Consider three vectors ¯p=^i+^j+^k,q=2^i+4^j^k and ¯r=^i+^j+3^k and let ¯s be a unit vector then ¯p,¯q and ¯r are

A
Linearly dependent
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B
Can form the sides of a possible triangle
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C
Such that the vectors (¯q¯r) is orthogonal to ¯p
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D
None of the above
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Solution

The correct option is D Such that the vectors (¯q¯r) is orthogonal to ¯p
qr
=¯i+3¯j4¯k

Now (qr).(¯r)
=(¯i+3¯j4¯k).(¯i+¯j+¯k)
=1+34
=0
Hence correct option is C.

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