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Determine the angles made by the vector V = (-36)i + (29)j with the positive x- and y-axes (enter the smallest possible positive values). Write the unit vector n in the direction of V.

User Nafeeza
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Answer:

Step-by-step explanation:


\overrightarrow{V}=-36\widehat{i}+29\widehat{j}

Let the given vector makes an angle θ from positive X axis


tan\theta =(vertical component)/(horizontal component)=\frac {29}{-36}

tanθ = -0.8055

θ = -38.85° from + X axis, i.e. 321.15° from + X axis in counter clock wise direction

Angle made from + y axis = 321.15° - 90° = 231.15°

Magnitude of V =
\sqrt{\left ( -36 \right )^(2)+\left ( 29 \right )^(2)=46.23

The unit vector in the direction of V is given by


\widehat{n}=\frac {\overrightarrow{V}}{V}


\widehat{n}=\frac{-36\widehat{i}+29\widehat{j}}{46.23}

User Cubed Eye
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