Question

the angle made by vector A =4i +3j with x axis is​

Answer 1

) in. 4i+3j is the vector joining the points (0,0) and 4 3

the 2D planeClearly, this vector lies in the 1st Quadrant

Clearly, the slope of this line is 3/4  and so the (acute) angle it makes with the x - axis will be:

atan(3/4) =36

Explanation:

Answer 2

Answer:

Required angle is

${cos}^{ - 1} \frac{3}{5} .$

Explanation:

The equation of the x axis is given by î [ Because in x axis y=0 .So, equation of x axis is i ]

and we have the other vector 4î+ 3ĵ.

The angle between two vectors is given by:

$\cos(x) = \frac{â.b̂}{ |â.b̂| }$

$= \frac{(4î+ 3ĵ).î}{( \sqrt{ {4}^{2} + {3}^{2}) } \times 1 }$

= $\frac{3}{5}$

Therefore

$\cos(x) = \frac{3}{5}$

$x = {cos}^{ - 1} \frac{3}{5}$

Required angle is

${cos}^{ - 1} \frac{3}{5}$