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Consider three vectors vecp=hati+hatj+ha...

Consider three vectors `vecp=hati+hatj+hatk,vecq=2hati+4hatj-hatk and vecr=hati+hatj+3hatk` and let `vecs` be a unit vector, then `vecp,vecq and vecr` are

A

linealy dependent

B

can form the sides of a possible triangle

C

such that the vectors (q-r) is orthogonal to p

D

such that each one of these can be expressed as a linear combination of the other two

Text Solution

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The correct Answer is:
C
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  • Consider three vectors vecp=hati+hatj+hatk, vecq=3hati-hatj+hatk and vecr=alpha hati+betahatj+lambdahatk, AA alpha, beta, lambda in R . If [(vecp,vecq,vecr)] is maximum and [vecr]=2sqrt6 , then the value of alpha-beta-lambda is equal to

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