The area occupied by the triangle will be half of the modulus of the cross product of the adjacent sides of the triangle.Hence the required area will be Area =
1
2
|
→
a
×
→
b
|
→
a
×
→
b
=(
∧
i
∧
j
∧
k
−2
3
2
−4
5
2
) =
∧
i
(−4)−
∧
j
(4)+
∧
k
(2) =−4
∧
i
−4
∧
j
+2
∧
k
→
a
×
→
b
2
=2
∧
i
−2
∧
j
+1
∧
k
|
→
a
×
→
b
2
|=√4+4+1=3 Area =
1
2
|
→
a
×
→
b
|=3 sq.units Thus, the area occupied by the triangle is 3 sq units.