UPSC NDA Math Model Paper 4

Given, the angle between

→

a

and

→

b

is

2π

3

and the projection of

→

a

in the direction of

→

b

is -2
We know that,
projection of

→

a

in the direction of

→

b

=

1

| → b |

(

→

a

.

→

b

)
⇒−2=

1

| → b |

(|

→

a

||

→

b

|‌cos‌

2π

3

)
⇒−2=|

→

a

|cos‌

2π

3

⇒−2=|

→

a

|(

−1

2

)
⇒|

→

a

|=4
Hence, if the angle between

→

a

and

→

b

is

2π

3

and the projection of

→

a

in the direction of

→

b

is -2 , then |

→

a

|=4