UPSC NDA Math Model Paper 10

Here, Let A = (0,2,2), B = (2,0,-1) and C =(3,4,0)
AB = (2-0, 0-2, -1-2) = (2, -2, -3) and
AC = (3-0, 4-2, 0-2) = (3, 2, -2)
Area of triangle =

1

2

×|

→

AB

×

→

AC

=

1

2

|

^ i	^ j	^ k
2	−2	−3
3	2	−2

|
=

1

2

|[

^

i

(4+6)+

^

j

(−4+9)+

^

k

(4+6)]|
=1∕2(10i+5j+10k)
=1∕2√(100+25+100)
= 15/2 sq unit
Hence, option (1) is correct.