Find with help of vectors area of triangle whose vertices are A(3,-1,2) B(1,-1-3) C(4,-3,1)
Answers
Answered by
0
Answer:
Given:A(1,2,3),B(2,−1,4) and C(4,5,−1)
Area of triangle ABC=
2
1
∣
∣
∣
∣
AB
×
AC
∣
∣
∣
∣
We have
AB
=
OB
−
OA
=(2−1)
i
^
+(−1−2)
j
^
+(4−3)
k
^
=
i
^
−3
j
^
+
k
^
AC
=
OC
−
OA
=(4−1)
i
^
+(5−2)
j
^
+(−1−3)
k
^
=3
i
^
+3
j
^
−4
k
^
AB
×
AC
=
∣
∣
∣
∣
∣
∣
∣
∣
i
^
1
3
j
^
−3
3
k
^
1
−4
∣
∣
∣
∣
∣
∣
∣
∣
=(12−3)
i
^
−(−4−3)
j
^
+(3+9)
k
^
=9
i
^
+7
j
^
+12
k
^
Magnitude of
AB
×
AC
=
(9)
2
+(7)
2
+12
2
∣
∣
∣
∣
AB
×
AC
∣
∣
∣
∣
=
81+49+144
=
274
Area of △ABC=
2
1
∣
∣
∣
∣
AB
×
AC
∣
∣
∣
∣
=
2
1
×
274
=
2
274
sq.units
∴ the required area is
2
274
sq.units
Similar questions