Respuesta :
Answer:
angle made by the vector with positive x axis,
[tex]\theta\ =\ 49.51^o[/tex]
the angle by the positive direction of y axis,
[tex]\alpha\ =\ 40.48^o[/tex]
unit vector in the direction of the given vector,
[tex]\hat{n}\ =\ \dfrac{(-35)i+(-41)j}{53.9}[/tex]
Step-by-step explanation:
Given vector is
[tex]\vec{V}=\ (-35)i\ +\ (-41)j[/tex]
we have to calculate the angle made by the vector with positive x and y axis,
The angle made by the vector with positive x axis can be given by,
[tex]tan\theta\ =\ \dfrac{-41}{-35}[/tex]
[tex]=>\ \theta\ =\ tan^{-1}\dfrac{-41}{-35}[/tex]
[tex]=>\ \theta\ =\ 49.51^o[/tex]
And the angle by the positive direction of y axis can be given by
[tex]\alpha\ =\ 90^o-\theta[/tex]
[tex]=\ 90^o-49.51^o[/tex]
[tex]=\ 40.48^o[/tex]
Now, we will calculate the unit vector in the direction of the given vector.
So,
[tex]\hat{n}\ =\ \dfrac{\vec{A}}{|\vec{A}|}[/tex]
[tex]=\ \dfrac{(-35i)+(-41)j}{\sqrt{(-35)^2+(-41)^2}}[/tex]
[tex]=\ \dfrac{(-35)i+(-41)j}{53.9}[/tex]
