A) (- 3, 1, 1)
B) (-3, 0, -1)
C) (3, 3, -1)
D) (3, 2, 1)
Correct Answer: D
Solution :
Plane passes through \[(x+y+z-1)+\,\,\lambda \,\,(2x\,+3y\,\,-z\,\,+\,\,4)\,\,=\,\,0\] & parallel to y-axis is \[x(1+2\,\lambda )\,\,+\,\,y(1+3\lambda )\,\,+z(1-\lambda )\,\,+\,\,(4\,\lambda -1)\,\,=\,\,0\] parallel to y axis \[3\,\lambda \,\,=-\,1\] \[\lambda \,\,=\,\,\,\frac{-1}{3}\] \[x\left( 1-\frac{1}{2} \right)\,+\,z\,\left( 1+\frac{1}{3} \right)\,\,+\,\,\left( -\frac{4}{3}-1 \right)\,\,=\,\,0\] \[x\left( \frac{1}{3} \right)\,\,+\,\,z\,\left( \frac{4}{3} \right)\,\,-\,\,\frac{7}{3}\,\,=\,\,0\] \[x+4z-7=0\] option check \[\left( -3,\text{ }1,\,\,1 \right)~~=-3+4-7x\] 5 \[\left( -3,\,\,0,\,\,-1 \right)=-\,3-4-7x\] 5 \[(3,\,\,\,3,\,\,-1)\,\,=\,\,3-4-7\text{x}\] 5 \[(3,\,\,2,\,\,1)\,\,\,=\,\,3+4\,\,-\,\,7\,\,=\,\,0\] 3
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