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Byju's Answer
Standard XII
Mathematics
Applications of Dot Product
Let λ, 2,1 be...
Question
Let
(
λ
,
2
,
1
)
be a point on the plane which passes through the point
(
4
,
–
2
,
2
)
.
If the plane is perpendicular to the line joining the points
(
–
2
,
–
21
,
29
)
and
(
–
1
,
–
16
,
23
)
,
then
(
λ
11
)
2
−
4
λ
11
−
4
is equal to
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Solution
−
−
→
A
B
⊥
−
−
→
P
Q
⇒
[
(
4
−
λ
)
^
i
−
4
^
j
+
^
k
]
⋅
[
^
i
+
5
^
j
−
6
^
k
]
=
0
⇒
4
−
λ
−
20
−
6
=
0
⇒
λ
=
−
22
Now,
λ
11
=
−
2
∴
(
λ
11
)
2
−
4
λ
11
−
4
=
4
+
8
−
4
=
8
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1
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Q.
Let
(
λ
,
2
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)
be a point on the plane which passes through the point
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4
,
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,
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If the plane is perpendicular to the line joining the points
(
–
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,
–
21
,
29
)
and
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