UPSC NDA I 2015 Mathematics Solved Paper

The magnitude of two vectors is given. However, the angle included between them is not specified. The given sum of the vectors will provide us the cosine of the unknown angle.
Hence, by applying the formula for vector addition, we get
|

→

a

+

→

b

=10√3|
√a2+b2+2abcosθ=10√3
a2+b2+2abcosθ=300
49+121+2(77)cosθ=300
154cosθ=130...(1)
Hence the magnitude of the subtraction of the two vectors is given by
|

→

a

−

→

b

|
=√a2+b2−2abcosθ
=√49+121−154cosθ
=√170−130  ....from(1)
=2√10