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Find the all the values of lamda such th...

Find the all the values of lamda such that `(x,y,z)!=(0,0,0)`and `x(hati+hatj+3hatk)+y(3hati-3hatj+hatk)+z(-4hati+5hatj)=lamda(xhati+yhatj+zhatk)`

A

A. `-2,0`

B

B `0,-2`

C

C. `-1,0`

D

D. `0,-1`

Text Solution

Verified by Experts

The correct Answer is:
D
Comparing the coefficient of `hati,hatj and hatk`, and the corresponding equations are
`x+3y-4z-lamdax` or `(1-lamda)x+3y-4z=0` . . . (i)
`x-(lamda+3)y+5z=0` . . . (ii)
`3x+y-lamdaz=0` . . . (iii)
These eqs. (i), (ii) and (iii) have a non-trivial solution, if
`|((1-lamda),3,-4),(1,-(lamda+3),5),(3,1,-lamda)|=0implies lamda =0,-1`
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