Question

The lines $x+y+z-3=0=2x-y+5z-6$ and $x-y-z+1=0=2x+3y+7z-k$ are coplanar then k equal

• A. $10$
• B. $11$
• C. $12$
• D. $13$

Answer 1

The correct option is B $11$

$x+y+z=3$

$2x-y+5z=6$

______________

$3x+6z=9$

$x+2z=3$ ___ (1)

$3(x-y-z+1=0)$

$2x+3y+7z=k$

$3x-3y-3z=-3$

_______________

$5x+4z=k-3$

$x-y-z+1=0$

$x+y+z-3=0$

_____________

$2x-2=0$

$1+2z=3$

$x=1$

$y=1$

$z=1$

$2x+3y+7z=k=12$ Ans