UPSC NDA Math Model Paper 10

Let that vector be

^

i

+

^

j

Let's find angle between

^

i

+

^

j

and

^

i

+3

^

j

cos‌θ1=

(1)(1)+(1)(3)

√1+4√1+1

=

1+3

√20

=

4

√4×5

=

2

√5

Let's find angle between

^

i

+

^

j

and 3

^

i

+

^

j

cos‌θ2=

(1)(3)+(1)(1)

√1+1√1+4

=

1+3

√20

=

4

√4×5

=

2

√5

Here cos‌θ1=cos‌θ2So, vector i+j is equally inclined to

^

i

+3

^

j

and 3

^

i

+

^

j

Hence, option (1) is correct.