Question

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. `-2,0`
B. `0,-2`
C. `-1,0`
D. `0,-1`

Answer 1

Correct Answer - 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`