UPSC NDA Math Model Paper 9

Given:

→

a

=3

^

i

+

^

j

+4

^

k

and

→

b

=

^

i

−

^

j

+

^

k

are the adjacent sides of a parallelogram
As we know that, if

→

a

=a1

^

i

+a2

^

j

+a3

^

k

and

→

b

=b1

^

i

+b2

^

j

+b3

^

k

then

→

a

×

→

b

=|

^ i	^ j	^ k
a1	a2	a3
b1	b2	b3

|
⇒

→

a

×

→

b

=|

^ i	^ j	^ k
3	1	4
1	−1	1

| =5

^

i

+

^

j

−4

^

k

As we know that, If

→

a

and

→

b

are the adjacent sides of a parallelogram, then area of parallelogram is given by: |

→

a

×

→

b

|
⇒|

→

a

×

→

b

|=√52+12+(−4)2 =√42
Hence, option C is the correct answer.