Question

the angle that the vector OA=5i^+5j^ make with y axis​

Answer 1

Answer:

yes it can be you can make

Answer 2

Answer:

The required angle is $\alpha=45^\circ$

Explanation:

To find : What is the angle made by vector of 0A=5i +5j with y axis?  

Solution :

First we find the magnitude of the vector,

$|\vec{OA}|=|\sqrt{A_x^2+A_y^2+A_z^2}|$

$|\vec{OA}|=|\sqrt{5^2+5^2+0^2}|$

$|\vec{OA}|=|\sqrt{25+25+0}|$

$|\vec{OA}|=\sqrt{50}$

$|\vec{OA}|=5\sqrt{2}$

Now, we find the angles between them,

$\cos\alpha=\frac{A_x}{|\vec{OA}|}$

$\cos\alpha=\frac{5}{5\sqrt{2}}$

$\cos\alpha=\frac{1}{\sqrt{2}}$

$\sin\alpha=\frac{A_y}{|\vec{OA}|}$

$\sin\alpha=\frac{5}{5\sqrt{2}}$

$\sin\alpha=\frac{1}{\sqrt{2}}$

$\tan\alpha=\frac{5}{5}$

$\tan\alpha=1$

$\tan\alpha=\tan(45)$

$\alpha=45$

Therefore, The required angle is $\alpha=45^\circ$