QJEEM22Ma65e1: JEE Main 2022 Mathematics - Class 12 JEEM22Ma65e1 Solution: Let and be two points on the line at a distance from the point…

$L:{{x + 1} \over 2} = {{y + 2} \over 3} = {{2 - 1} \over 2}$

Let $T(2t - 1,\,3t - 2,\,2t + 1)$

$\because$ $PT\,{ \bot ^r}\,QR$

$\therefore$ $2(2t - 5) + 3(3t - 4) + 2(2t - 6) = 0$

$17t = 34$

$\therefore$ $t = 2$

So $T(3,4,5)$

$\therefore$ $PT = \sqrt {1 + 4 + 4} = 3$

$\therefore$ $QT = \sqrt {26 - 9} = \sqrt {17}$

$\therefore$ Area of $\Delta PQR = {1 \over 2} \times 2\sqrt {17} \times 3 = 3\sqrt {17}$

$\therefore$ Square of $ar(\Delta PQR) = 153$ .