UPSC NDA Math Model Paper 1

Concept:
Let

→

a

and

→

b

be the two vectors,
Dot product of two vectors is given by:

→

a

⋅

→

b

=|

→

a

||

→

b

|cos‌θ
Cross product of two vectors is given by:

→

a

×

→

b

=|

→

a

||

→

b

|sinθ

∧

n

, where

∧

n

is a unit vector
Calculation:
Given: |

→

a

×

→

b

|=|

→

a

|

→

b

|cosθ
To Find: Angle between

→

a

adn

→

b

|

→

a

×

→

b

|=|

→

a

⋅

→

b

|
⇒|

→

a

||

→

b

|sin‌θ|

∧

n

|=|

→

a

||

→

b

|cos‌θ
⇒sin‌θ=cos‌θ‌‌(∵|

∧

n

|=1)
⇒tan‌θ=1
∴θ=45∘