KVPY Sample Paper KVPY Stream-SX Model Paper-10

Consider the planes \[3x-6y+2z+5=0\] and \[4x-12y+3z=3.\] The plane \[67x-162y+47z+44=0\] bisects the angle between the planes which

A) contains origin

B) is right angle

C) is obtuse

D) none of these

Correct Answer: D

Solution :

\[3x-6y+2z+5=0\]	..(i)
\[-\,4x+12y-3z+3=0\]	..(ii)
\[{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}}=-12-72-6<0\]
hence '+' sign bisector is origin containing and is also acute angle bisector
\[\therefore \] \[\frac{3x-6y+2z+5}{7}=\frac{+\,(-\,4x+12y-3z+3)}{13}\]
\[67x-162y+47z+44=0\]