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find the value of m for which the line r i 2k 2i m
Question:
Find the value of
m
for which the line
r
→
=
(
i
^
+
2
k
^
)
+
λ
(
2
i
^
−
m
j
^
−
3
k
^
)
is parallel to the plane
r
→
⋅
(
m
i
^
+
3
j
^
+
k
^
)
=
4
?
MHT CET
Updated On:
Aug 14, 2024
(A) 2
(B) -2
(C) 3
(D) -3
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Verified By Collegedunia
The Correct Option is
D
Solution and Explanation
Explanation:
Given: Equation of line
r
→
=
(
i
^
+
2
k
^
)
+
λ
(
2
i
^
−
m
j
^
−
3
k
^
)
and equation of plane
r
→
⋅
(
m
i
^
+
3
j
^
+
k
^
)
=
4
It is given that the given line is parallel to the given plane,As we know that, if the line
r
→
=
a
→
+
λ
b
→
is parallel to the plane
r
→
⋅
n
→
=
q
then
b
→
⋅
n
→
=
0
Here,
b
→
=
2
i
^
−
m
j
^
−
3
k
^
and
n
→
=
m
i
^
+
3
j
^
+
k
^
⇒
b
→
⋅
n
→
=
2
m
−
3
m
−
3
=
0
⇒
m
=
−
3
Hence, the correct option is (D).
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