A) \[\left( -\sqrt{2},1,-4 \right)\]
B) \[\left( \sqrt{2},1,4 \right)\]
C) \[\left( \sqrt{2},-1,4 \right)\]
D) \[\left( -\sqrt{2},-1,-4 \right)\]
Correct Answer: B
Solution :
Let \[ax+by+cz=1\]be the equation of the plane \[\Rightarrow 0-b+0=1\]\[\Rightarrow b=-1\] \[0+0+c=1\]\[\Rightarrow c=1\] \[\cos \theta =\left| \frac{\vec{a}.\vec{b}}{\left| {\vec{a}} \right|\left| {\vec{b}} \right|} \right|\] \[\frac{1}{\sqrt{2}}=\frac{\left| 0-1-1 \right|}{\sqrt{\left( {{a}^{2}}+1+1 \right)}\sqrt{0+1+1}}\] \[\Rightarrow {{a}^{2}}+2=4\]\[\Rightarrow a=\pm \sqrt{2}\]\[\Rightarrow \pm \sqrt{2}x-y+z=1\] Now for -sign \[-\sqrt{2}.\sqrt{2}-1+4=1\] option [b]
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