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AP EAPCET 08-Jul-2022 Shift 1 Paper
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© examsnet.com
Question : 33
Total: 160
A. B. C. D are any 4 points and
|
A
B
×
C
D
+
B
C
×
A
D
+
C
A
×
B
D
|
=
λ
(" Area of △ ABC ) then "
λ
=
1
2
3
4
Validate
Solution:
👈: Video Solution
Let position vector of
A
,
B
,
C
and
D
are
a
,
b
,
c
and
d
respectively.
|
A
B
×
C
D
+
B
C
×
A
D
+
C
A
×
B
D
|
=
λ
(
Area
of
Δ
A
B
C
)
⇒
|
(
b
−
a
)
×
(
d
−
c
)
+
(
c
−
b
)
×
(
d
−
a
)
+
(
a
−
c
)
×
(
d
−
b
)
|
=
λ
2
|
a
×
b
+
b
×
c
+
c
×
a
|
|
(
b
×
d
)
−
(
a
×
d
)
+
(
a
×
c
)
+
(
c
×
d
)
−
(
c
×
a
)
−
(
b
×
a
)
+
(
a
×
d
)
−
(
a
×
b
)
−
(
c
×
d
)
+
(
c
×
b
)
|
⇒
2
|
a
×
b
+
b
×
c
+
c
×
a
|
=
λ
2
|
a
×
b
+
b
×
c
+
c
×
a
|
⇒
λ
4
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