question_answer

Let Q be the foot of perpendicular from the origin to the plane \[4x-3y+z+13=0\] and R be a point \[(-1,\,1,-6)\] on the plane. The length QR is

A)  \[3\sqrt{\frac{7}{2}}\]

B)  \[\sqrt{14}\]

C)  \[\sqrt{\frac{19}{2}}\]                                  

D)  \[\frac{3}{\sqrt{2}}\]  

Correct Answer: A

Solution :

\[OQ=\frac{13}{\sqrt{26}}\]                                 \[OR=\sqrt{38}\] \[\therefore QR=\sqrt{{{(OR)}^{2}}-{{(OQ)}^{2}}}\] \[=\sqrt{\frac{63}{2}}=3\sqrt{\frac{7}{2}}\]