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KCET 2016 Math Solved Paper
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© examsnet.com
Question : 57
Total: 60
Find the co-ordinates of the foot of the perpendicular drawn from the origin to the plane 5y + 8 = 0 :
(
0
,
−
18
5
,
2
)
(
0
,
8
5
,
0
)
(
8
25
,
0
,
0
)
(
0
,
−
8
5
,
0
)
Validate
Solution:
Given equation of plane:
5
y
+
8
=
0
So,
→
N
=
(
0
,
5
,
0
)
Equation of line passes through origin and is perpendicular to this plane is given by
x
0
=
y
5
=
z
0
=
λ
Foot of the perpendicular is found by intersection of line with plane. So,
x
=
0
,
y
=
5
λ
,
z
=
0
Now,
25
λ
+
8
=
0
⇒
λ
=
−
8
25
Therefore, point is
(
0
,
−
8
5
,
0
)
© examsnet.com
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