QJEEM20Ma6fa0: JEE Main 2020 Mathematics - Class 12 JEEM20Ma6fa0 Solution: If the foot of the perpendicular drawn from the point (1, 0, 3) …

Direction Ratio of PQ are

= ( ${5 \over 3} - 1$ , ${7 \over 3} - 0$ , ${{17} \over 3} - 3$ )

= (2, 7, 8)

Direction ratio of line QA are

= ( $\alpha - {5 \over 3}$ , $7 - {7 \over 3}$ , 1 - ${{17} \over 3}$ )

= (3 $\alpha$ – 5, 14, –14)

PQ is perpendicular to line QA

$\therefore$ $\overrightarrow {PQ} .\overrightarrow {QA}$ = 0

$\Rightarrow$ 2(3 $\alpha$ – 5) + 7.14 + (–14).8 = 0

$\Rightarrow$ $\alpha$ = 4