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Test Index
Vector Algebra Part 3
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Section:
Mathematics
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© examsnet.com
Question : 47
Total: 54
The distance of the point
Q
(
0
,
2
,
−
2
)
form the line passing through the point
P
(
5
,
−
4
,
3
)
and perpendicular to the lines
→
r
=
(
−
3
^
i
+
2
^
k
)
+
λ
(
2
^
i
+
3
^
j
+
5
^
k
)
,
λ
∈
ℝ
and
→
r
=
(
^
i
−
2
^
j
+
^
k
)
+
µ
(
−
^
i
+
3
^
j
+
2
^
k
)
,
µ
∈
ℝ
is
[31-Jan-2024 Shift 1]
√
86
√
20
√
54
√
74
Validate
Solution:
👈: Video Solution
A vector in the direction of the required line can be obtained by cross product of
|
^
i
^
j
^
k
2
3
5
−
1
3
2
|
=
−
9
^
i
−
9
^
j
+
9
^
k
Required line,
→
r
=
(
5
^
i
−
4
^
j
+
3
^
k
)
+
λ
′
(
−
9
^
i
−
9
^
j
+
9
^
k
)
→
r
=
(
5
^
i
−
4
^
j
+
3
^
k
)
+
λ
(
^
i
+
^
j
−
^
k
)
Now distance of
(
0
,
2
,
−
2
)
P
.
V
.
of
P
≡
(
5
+
λ
)
^
i
+
(
λ
−
4
)
^
j
+
(
3
−
λ
)
^
k
→
AP
=
(
5
+
λ
)
^
i
+
(
λ
−
6
)
^
j
+
(
5
−
λ
)
^
k
→
AP
⋅
(
^
i
+
^
j
−
^
k
)
=
0
5
+
λ
+
λ
−
6
−
5
+
λ
=
0
λ
=
2
|
→
AP
|
=
√
49
+
16
+
9
|
→
AP
|
=
√
74
© examsnet.com
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