UPSC NDA I 2015 Mathematics Solved Paper

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.