A) \[\frac{13}{\sqrt{21}}\]
B) \[\frac{13}{21}\]
C) \[\frac{13}{3\sqrt{21}}\]
Correct Answer: A
Solution :
We know that the perpendicular distance of a point P with position vector \[\mathbf{a}\] from the plane \[\mathbf{r}.\,\mathbf{n}=d\] is given by \[\frac{|\mathbf{a}.\mathbf{n}-d|}{|\mathbf{n}|}\]. Here \[\mathbf{a}=2\mathbf{i}+\mathbf{j}-\mathbf{k},\mathbf{n}=\mathbf{i}-2\mathbf{j}+4\mathbf{k}\] and \[d=9\]. So, required distance \[=\frac{|(2\mathbf{i}+\mathbf{j}-\mathbf{k}).(\mathbf{i}-2\mathbf{j}+4\mathbf{k})-9|}{\sqrt{1+4+16}}\] \[=\frac{|2-2-4-9|}{\sqrt{21}}=\frac{13}{\sqrt{21}}\]. \[\frac{3}{\sqrt{21}}\]
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