Question
Mathematics Question on Three Dimensional Geometry
What will be the distance of (1,0,2) from the point of intersection of plane x−y+z=16 and the line (3x−2)=(4y+1)=(12z−2) ?
A
13 units
B
17 units
C
25 units
D
19 units
Answer
13 units
Explanation
Solution
Given line is 3x−2
=4y+1
=12z−2=r(say) …(i)
Any point on (i) is P(3r+2,4r−1,12r+2)
The point P lies on x−y+z=16 …(ii)
∴3r+2−(4r−1)+12r+2=16
⇒11r=11
⇒r=1
Thus, the line cuts the plane at P(5,3,14).
The distance of Q(1,0,2) from P(5,3,14) is given by
PQ=(5−1)2+(3−0)2+(14−2)2
=16+9+144
=13 units