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Mathematics
Mathematics
Problem
Let
P
(
3
,
2
,
6
)
P(3, 2, 6)
P
(
3
,
2
,
6
)
be a point in space and
Q
Q
Q
be a point on the line
r
=
(
i
−
j
+
2
k
)
+
μ
(
−
3
i
+
j
+
5
k
)
\mathbf{r} = (\mathbf{i} - \mathbf{j} + 2\mathbf{k}) + \mu(-3\mathbf{i} + \mathbf{j} + 5\mathbf{k})
r
=
(
i
−
j
+
2
k
)
+
μ
(
−
3
i
+
j
+
5
k
)
. Then the value of
μ
\mu
μ
for which the vector
P
Q
PQ
P
Q
is parallel to the plane
x
−
4
y
+
3
z
=
1
x - 4y + 3z = 1
x
−
4
y
+
3
z
=
1
is a.
1
4
\frac{1}{4}
4
1
b.
−
1
4
-\frac{1}{4}
−
4
1
c.
1
8
\frac{1}{8}
8
1
d.
−
1
8
-\frac{1}{8}
−
8
1
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