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Question
Mathematics
Acute angel between the line (x-5/2) = (y+1/-1) = (z+4/1) and the plane 3x - 4y - z + 5 = 0 is
Q. Acute angel between the line
2
x
−
5
=
−
1
y
+
1
=
1
z
+
4
and the plane 3x - 4y - z + 5 = 0 is
5071
124
KCET
KCET 2019
Three Dimensional Geometry
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A
cos
−
1
(
2
13
5
)
28%
B
cos
−
1
(
364
9
)
30%
C
sin
−
1
(
2
3
5
)
29%
D
sin
−
1
(
364
9
)
16%
Solution:
dr’s of line 2, -1, 1
dr’s of normal to plane -3, 4, 1
s
in
θ
=
∣
∣
4
+
1
+
1
9
+
16
+
1
−
6
−
4
+
1
∣
∣
=
∣
∣
156
−
9
∣
∣
=
156
9
θ
=
s
i
n
−
1
(
156
9
)
=
s
i
n
−
1
(
2
39
9
)
=
co
s
−
1
(
2
13
5
)