Search any question & find its solution
Question:
Answered & Verified by Expert
If $(3,4,-7)$ is the foot of the perpendicular drawn from the point $(-2,3,6)$ to the plane $\pi$, then the sum of the intercepts made by the plane $\pi$ on the $X$ and $Y$-axes is
Options:
Solution:
1699 Upvotes
Verified Answer
The correct answer is:
132
DR's of plane is
$$
3+2,4-3,-7-6=5,1,-13
$$
Equation of plane is $5 x+y-13 z=d$
Plane passes through the point $(3,4,-7)$
$$
\begin{aligned}
& 15+4+91=d \\
& d=110 \\
&
\end{aligned}
$$
$\Rightarrow$
$\therefore$ Equation of plane is $5 x+y-13 z=110$
$$
\frac{5 x}{110}+\frac{y}{110}-\frac{13 z}{110}=1 \Rightarrow \frac{x}{22}+\frac{y}{110}+\frac{z}{\frac{-110}{13}}=1
$$
Sum of $x$-intercept and $y$-intercept
$$
=22+110=132
$$
$$
3+2,4-3,-7-6=5,1,-13
$$
Equation of plane is $5 x+y-13 z=d$
Plane passes through the point $(3,4,-7)$
$$
\begin{aligned}
& 15+4+91=d \\
& d=110 \\
&
\end{aligned}
$$
$\Rightarrow$
$\therefore$ Equation of plane is $5 x+y-13 z=110$
$$
\frac{5 x}{110}+\frac{y}{110}-\frac{13 z}{110}=1 \Rightarrow \frac{x}{22}+\frac{y}{110}+\frac{z}{\frac{-110}{13}}=1
$$
Sum of $x$-intercept and $y$-intercept
$$
=22+110=132
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.