Question

A line L passes through the point P(5, -6, 7) and is parallel to the planes x + y + z = 1 and 2x - y - 2z = 3.Find the direction ratios of the line of intersection of the given planes.

• A. $<11,-4,-9>$
• B. $<-1,-4,3>$
• C. $<1,-4,3>$
• D. $<1,-4,-3>$

Answer 1

The correct option is A $<11,-4,-9>$

A line L passes through the point $P(5,-6,7)$ and is parallel to the planes

$x+y+z=1$ ......(1)

$2x-y-2z=3$......(2)

the direction ratios of the line of intersection of the given planes =

$\Rightarrow$ $x+y+z=1,2x-y-2z=3$

$(x+y+z-1)+k(2x-y-2z-3)=0$ ......(3)

it passes through $(5,-6,7)$ substitute the value in eqn (3)

$(5-6+7-1)+k(10+6-14-3)=0$

$5+k(-1)=0$

$5-k=0$

$k=5$ ......(4)

substitute eqn (4) in (3) we will get:

$(x+y+z-1)+5(2x-y-2z-3)=0$

$\Rightarrow$ $x+y+z-1+10x-5y-10z-15=0$

$\Rightarrow$ $11x-4y-9z-16=0$

$\Rightarrow 11x-4y-9z=16$

which is the equation of a plane, hence the direction ratios of the line

of intersection of the given planes is equal to $<11,-4,-9>$