The vectors and have the same magnitude. The angle between the vectors is 125°, and the magnitude of their cross product is 20. What is ?
a) 4.08
b) 4.94
c) 16.4
d) 24.4
The vectors
\(\vec{a} \) \vec{a}
and
\(\vec{b} \) \vec{b}
have the same magnitude.
The angle between the vectors is 125\(^{\circ}\) ^{\circ},
and the magnitude of their cross product is 20.
I assume what is a ?
\(\begin{array}{|rcll|} \hline |\vec{a}\times \vec{b}| = 20 &=& a\cdot b \cdot \sin{(125^{\circ})} \quad & | \quad a =b \\ 20 &=& a\cdot a \cdot \sin{(125^{\circ})} \\ a\cdot a \cdot \sin{(125^{\circ})} &=& 20 \\ a^2\cdot \sin{125^{\circ}} &=& 20 \\ a^2 &=& \dfrac{20}{\sin{(125^{\circ})}} \\ a &=& \sqrt{\dfrac{20}{\sin{(125^{\circ})}}} \\ a &=& \sqrt{\dfrac{20}{0.81915204429}} \\ a &=& \sqrt{24.4154917752} \\ \mathbf{ a } & \mathbf{=} & \mathbf{4.94120347438} \\ \hline \end{array}\)