Three Dimensional Geometry

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