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Let alpha epsilon R and the three vector...

Let `alpha` `epsilon R` and the three vectors `veca=alpha hati+hatj+3hatk, vecb=2hati+hatj-alpha hatk` and `vecc=alpha hati-2hatj+3hatk`. Then the set `S={alpha: veca, vecb` and `vecc` are coplanat}:

A

contains exactly two positive numbers

B

contains exactly two numbers only one of which is positive

C

is empty

D

is singleton

Text Solution

Verified by Experts

The correct Answer is:
C
`|(alpha, 1,3),(2,1,-alpha),(alpha,-2,3)|=0`
`alpha(3-2alpha)-1(6+alpha^(2))+3(-4- alpha)=0`
`3alpha -2 alpha^(2)-6alpha^(2)-12-3alpha=0`
`3alpha^(2)=-18`
`alpha^(2)=-6`
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