+280 I got square root 113 for the first question.
How do i find the angle? do i to a tangent inverse?
+129845 tan (theta) = (7 / -8)
arctan (7/-8) = theta = -41.1859°
The terminal point of this vector lies in the second quadramt....so the angle is
180 - 41.1859 ≈ 138.81407° ≈ 138. 8141°
And this is the angle ( theta ) that the vector makes with the positive x axis
+26387 1. The magnitude of \(\vec{u}\).
Round your answer to at least four decimal places.
\(\vec{u} = \binom{-8}{7}\)
\(\begin{array}{|rcll|} \hline ||\vec{v}|| &=& \sqrt{(-8)^2+7^2} \\ &=& \sqrt{64+49} \\ &=& \sqrt{113} \\ &=& 10.6301458127 \\ &\approx& 10.6301 \\ \hline \end{array}\)
2.The direction of \(\vec{u}\), thaat is the angle \(\theta\) it makes with the positive x-axis.
State your answer in degrees, rounded to at least four decimal places.
\(\vec{u} = \binom{-8}{7} \)
\(\begin{array}{|rcll|} \hline \tan(\theta) &=& \frac{|~\vec{e_x} \times \vec{u}~| } {\vec{e_x} \cdot \vec{v} } \\ &=& \frac{ \left|~\binom{1}{0} \times \binom{-8}{7}~\right| } {\binom{1}{0} \cdot \binom{-8}{7} } \\ &=& \frac{ (1)\cdot (7) - (0)\cdot (-8) } { (1)\cdot (-8) + (0)\cdot (7) } \\ &=& \frac{ 7+0 } { -8+0 } \\ &=& \frac{ 7} { -8 } \quad & | \quad II.\text{Quadrant} \\ \theta &=& \arctan(\frac{ 7 } { -8 }) \\ \theta &=& \arctan(-0.875) \\ \theta &=& -41.1859251657^{\circ} + 180^{\circ} \quad & | \quad II.\text{Quadrant} \\ \theta &=& 138.814074834^{\circ} \\ \theta &\approx& 138.8141^{\circ} \\ \hline \end{array} \)
