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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

 May 23, 2018
 #1
avatar+22572 
+1

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 ? 

 

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

 

laugh

 May 24, 2018

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