KVPY Sample Paper KVPY Stream-SX Model Paper-11

If the lines \[x=ay+b,\]\[z=cy+d\] and \[x=a'z+b',\] \[y=c'z+d'\] are perpendicular, then:

A) \[cc'+a+a'=0\]

B) \[aa'+c+c'=0\]

C) \[ab'+bc'+1=0\]

D) \[bb'+cc'+1=0\]

Correct Answer: B

Solution :

Line \[x=ay+b\]

\[z=cy+d\]

\[\Rightarrow \] \[\frac{x-b}{a}=\frac{y}{1}=\frac{z-d}{c}\]

Line \[x=a'z+b'\]

\[y=c'z+d'\]

\[\Rightarrow \] \[\frac{x-b'}{a'}=\frac{y-d'}{c'}=\frac{z}{1}\]

Given both the lines are perpendicular \[\Rightarrow \] \[aa'+c'+c=0\]