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# 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

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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

Julius  May 23, 2018
#1
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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 ?

$$\begin{array}{|rcll|} \hline |\vec{a}\times \vec{b}| = 20 &=& a\cdot b \cdot \sin{(125^{\circ})} \quad & | \quad a =b \\ 20 &=& a\cdot a \cdot \sin{(125^{\circ})} \\ a\cdot a \cdot \sin{(125^{\circ})} &=& 20 \\ a^2\cdot \sin{125^{\circ}} &=& 20 \\ a^2 &=& \dfrac{20}{\sin{(125^{\circ})}} \\ a &=& \sqrt{\dfrac{20}{\sin{(125^{\circ})}}} \\ a &=& \sqrt{\dfrac{20}{0.81915204429}} \\ a &=& \sqrt{24.4154917752} \\ \mathbf{ a } & \mathbf{=} & \mathbf{4.94120347438} \\ \hline \end{array}$$

heureka  May 24, 2018