Search any question & find its solution
Question:
Answered & Verified by Expert
If the line joining $A(1,3,4)$ and $B$ is divided by the point $(-2,3,5)$ in the ratio $1: 3$, then $B$ is
Options:
Solution:
1148 Upvotes
Verified Answer
The correct answer is:
$(-11,3,8)$
Using internally ratio formula,
$$
\begin{aligned}
& (-2,3,5) \\
& =\left(\frac{1 \times x+3 \times 1}{1+3}, \frac{1 \times y+3 \times 3}{1+3}, \frac{1 \times z+3 \times 4}{1+3}\right) \\
\Rightarrow & (2,3,5)=\left(\frac{x+3}{4}, \frac{y+9}{4}, \frac{z+12}{4}\right) \\
\Rightarrow & x+3=-8, y+9=12, z=12=20 \\
\Rightarrow & x=-11, y=+3, z=8 \\
\therefore & \text { Required point }=B(-11,3,8)
\end{aligned}
$$
$$
\begin{aligned}
& (-2,3,5) \\
& =\left(\frac{1 \times x+3 \times 1}{1+3}, \frac{1 \times y+3 \times 3}{1+3}, \frac{1 \times z+3 \times 4}{1+3}\right) \\
\Rightarrow & (2,3,5)=\left(\frac{x+3}{4}, \frac{y+9}{4}, \frac{z+12}{4}\right) \\
\Rightarrow & x+3=-8, y+9=12, z=12=20 \\
\Rightarrow & x=-11, y=+3, z=8 \\
\therefore & \text { Required point }=B(-11,3,8)
\end{aligned}
$$
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.