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Byju's Answer
Standard XII
Mathematics
Applications of Cross Product
A = 0, 1, 2, ...
Question
A
=
(
0
,
1
,
2
)
,
B
=
(
3
,
0
,
1
)
,
C
=
(
4
,
3
,
6
)
,
D
=
(
2
,
3
,
2
)
are the rectangular cartesian co-ordinates. Find
the area of the triangle ABC.
A
√
90
,
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B
√
45
2
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C
45
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D
18
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Solution
The correct option is
B
√
90
,
Given,
A
=
(
0
,
1
,
2
)
,
B
=
(
3
,
0
,
1
)
,
C
=
(
4
,
3
,
6
)
,
D
=
(
2
,
3
,
2
)
⇒
→
A
B
=
(
3
−
0
)
i
+
(
0
−
1
)
j
+
(
1
−
2
)
k
⇒
→
A
B
=
3
i
−
1
j
−
1
k
⇒
→
A
C
=
(
4
−
0
)
i
+
(
3
−
1
)
j
+
(
6
−
2
)
k
⇒
→
A
C
=
4
i
+
2
j
+
4
k
⇒
Area of triangle ABC is
=
1
2
|
→
A
B
×
→
A
C
|
⇒
→
A
B
×
→
A
C
=
∣
∣ ∣
∣
i
j
k
3
−
1
−
1
4
2
4
∣
∣ ∣
∣
=
−
2
i
−
16
j
+
10
k
=
2
(
−
i
−
8
j
+
5
k
)
⇒
Required area is
=
1
2
|
→
A
B
×
→
A
C
|
=
√
90
Suggest Corrections
0
Similar questions
Q.
A
=
(
0
,
1
,
2
)
,
B
=
(
3
,
0
,
1
)
,
C
=
(
4
,
3
,
6
)
,
D
=
(
2
,
3
,
2
)
are the rectangular cartesian co-ordinates. Find
the volume of the tetrahedron ABCD.
Q.
The volume of the tetrahedron whose vertices are
(
0
,
1
,
2
)
,
(
3
,
0
,
1
)
,
(
4
,
3
,
6
)
and
(
2
,
3
,
2
)
is equal to
Q.
The volume of the tetrahedron whose vertices are
(
0
,
1
,
2
)
,
(
4
,
3
,
6
)
,
(
2
,
3
,
2
)
and
(
3
,
0
,
1
)
is
(
in unit
3
)
Q.
In a
△
A
B
C
, if
cos
A
cos
B
cos
C
=
√
3
−
1
8
and
sin
A
sin
B
sin
C
=
3
+
√
3
8
, then the angles of the triangle are
Q.
In a triangle ABC,
∠
ABC +
∠
BCA = 120
°
. Find the value of
∠
CAB.
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