Question

Determine the angles made by the vector V= (-35)i + (-41)j with the positive x-and y-axes. Write the unit vector n in the direction of V. Answers: ex= 9,0y i n =

Answer 1

angle made by the vector with positive x axis,

`\theta\ =\ 49.51^o`

the angle by the positive direction of y axis,

`\alpha\ =\ 40.48^o`

unit vector in the direction of the given vector,

`\hat{n}\ =\ ((-35)i+(-41)j)/(53.9)`

Explanation:

Given vector is

`\vec{V}=\ (-35)i\ +\ (-41)j`

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,

`tan\theta\ =\ (-41)/(-35)`

`=>\ \theta\ =\ tan^(-1)(-41)/(-35)`

`=>\ \theta\ =\ 49.51^o`

And the angle by the positive direction of y axis can be given by

`\alpha\ =\ 90^o-\theta`

`=\ 90^o-49.51^o`

`=\ 40.48^o`

Now, we will calculate the unit vector in the direction of the given vector.

So,

`\hat{n}\ =\ \frac{\vec{A}}{|\vec{A}|}`

`=\ ((-35i)+(-41)j)/(√((-35)^2+(-41)^2))`

`=\ ((-35)i+(-41)j)/(53.9)`