UPSC NDA I 2021 Mathematics Solved Paper

CONCEPT:
The scalar product of two vectors a and

→

b‌ is given by ‌

→

a

⋅

→

b

=|

→

a

|×|b|cos‌θ
CALCULATION:
Given: Vector

→

r

=a

∧

i

+b

∧

j

is equally inclined to both x and y axes and the magnitude of the vector is 2 units. i.e |r|=2
⇒√a2+b2=2
⇒a2+b2=4
∵ The vector

→

r

=a

∧

i

+b

∧

j

‌‌ is equally inclined to both x and y axes
Let θ be the angle between the vector

→

r

=a

∧

i

+b

∧

j

and both the x and y axes.
⇒cos‌θ=‌

a

2

=‌

b

2

⇒a=b
So, by substituting a=b in equation (1), we get
⇒2b2=4⇒b=√2
So, a=b=√2
Hence, correct option is 3