Q37 / 100 · BITSAT 2023 (Memory Based Paper 2) · Mathematics
If the co-ordinates of the point in which the line joining the points $(3,5,-7)$ and $(-2,1,8)$ is intersected by the plane $y z$ is $\left[\mathrm{a}, \frac{13}{\mathrm{~b}}, \mathrm{c}\right]$, then $(a+b-c)=$
- A
2 - Correct answerB
3 - C
4 - D
5
Solution
Ratio $=-\left(\frac{3}{-2}\right)=\frac{3}{2}$
$\therefore \quad$ Required co-ordinates of the points are
$\begin{aligned}<br />& {\left[\frac{6-6}{5}, \frac{10+3}{5}, \frac{-14+24}{5}\right]=\left(0, \frac{13}{5}, 2\right) .} \\<br />& \therefore a+b-c=0+5-2=3<br />\end{aligned}$
$\therefore \quad$ Required co-ordinates of the points are
$\begin{aligned}<br />& {\left[\frac{6-6}{5}, \frac{10+3}{5}, \frac{-14+24}{5}\right]=\left(0, \frac{13}{5}, 2\right) .} \\<br />& \therefore a+b-c=0+5-2=3<br />\end{aligned}$
Hence, the correct answer is option: 'B'.