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Byju's Answer
Standard XII
Mathematics
Area of Triangle Using Coordinates
Using vectors...
Question
Using vectors find the area of the triangle with vertices, A (2, 3, 5), B (3, 5, 8) and C (2, 7, 8).
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Solution
Let
a
→
,
b
→
and
c
→
be
the
position
vector
s
of
A
,
B
and
C
,
respectively
.
Then
,
a
→
=
2
i
^
+
3
j
^
+
5
k
^
b
→
=
3
i
^
+
5
j
^
+
8
k
^
c
→
=
2
i
^
+
7
j
^
+
8
k
^
Now
,
A
B
→
=
b
→
-
a
→
=
i
^
+
2
j
^
+
3
k
^
A
C
→
=
c
→
-
a
→
=
0
i
^
+
4
j
^
+
3
k
^
∴
A
B
→
×
A
C
→
=
i
^
j
^
k
^
1
2
3
0
4
3
=
-
6
i
^
-
3
j
^
+
4
k
^
⇒
A
B
→
×
A
C
→
=
36
+
9
+
16
=
61
Area of triangle
ABC
=
1
2
A
B
→
×
A
C
→
=
61
2
sq. units
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Q.
Using vectors, find the area of the triangle with vertices:
(i) A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5)
(ii) A(1, 2, 3), B(2, −1, 4) and C(4, 5, −1) [CBSE 2011, NCERT EXEMPLAR]
Q.
Find the area of triangle whose vectors are (1,1,1), (2,1,3)and (0,0,1) using vectors .
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