Question

If Ā =3i+5j then tan 0 : = ​

Answer 1

Given :   Ā =3i+5j

θ is the angle made with x axis

To Find : Tanθ

Solution:

Ā =3i+5j

3 and 5 both are positive

Hence θ lies in 1st Quadrant

=> Tanθ = 5/3

Another method

θ is the angle made with x axis  

Let say another vector   i

A.B  = |A||B|Cosθ

A = 3i+5j

B = i

=> (3i+5j).(i)  =(√3² + 5²)(1) Cosθ

=> 3 =  √34 Cosθ

=> 1/Cosθ =  √34/3

=> Secθ =  √34/3

=> Sec²θ =   34/9

=> 1 + tan²θ =   34/9

=> tan²θ =   25/9

=> tanθ =    5/3

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