We know that YZ plane divides PQ in the ratio 2:3. By section formula the intersecting point is (‌
3a+6
5
,‌
12+2β
5
,‌
21+16
5
) On Y plane, x-coordinate of any point is zera. ⇒3α+6=0⇒α=−2 ∴ Coordinate of P is (−24,7) Also, 2X plane divides PQ in ratio 4:5. The intersecting point is (‌
12+5a
9
,‌
4β+20
9
,‌
32+35
9
) On 2x plane, y-coordinate of any point is 0 . ⇒‌‌4β+20=0⇒β=−5 ∴ Coordinate of Q is (3,−5.8) PQ‌=√13+2)2+(−5−4)2+(8−7)2 ‌=√25+81+1 ‌=√107