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# ​ Vector Problem

+1
345
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+956

Really confused on this one.

May 2, 2018

#1
+22343
+2

Vector Problem

$$\begin{array}{|rcll|} \hline && |3\vec{x}+2\vec{y}| \qquad \text{Formula: |\vec{v}|=\sqrt{\vec{v}\cdot \vec{v}} } \\\\ &=& \sqrt{ (3\vec{x}+2\vec{y}) (3\vec{x}+2\vec{y}) } \\ &=& \sqrt{ 9\vec{x}^2 + 4 \vec{y}^2 + 2\cdot 3 \cdot 2\cdot( \vec{x}\cdot \vec{y}) } \\\\ && \qquad \text{Formula: |\vec{x}^2|=|\vec{x}|^2 = x^2 \qquad |\vec{y}^2|=|\vec{y}|^2 = y^2 } \\\\ &=& \sqrt{ 9x^2 + 4 y^2 + 12 \cdot(\vec{x}\cdot \vec{y}) } \\\\ && \qquad \text{unit vectors: |\vec{x}|=x=1 \quad|\vec{y}|=y=1} \\\\ &=& \sqrt{ 9 + 4 + 12 \cdot (\vec{x}\cdot \vec{y}) } \\\\ && \qquad \text{Formula: \vec{x}\cdot \vec{y} = |\vec{x}|\cdot |\vec{y}| \cdot \cos(120^{\circ})=1\cdot 1\cdot (-0.5)=-0.5  } \\\\ &=& \sqrt{ 9 + 4 + 12 \cdot (-0.5) } \\\\ &=& \sqrt{ 13 -6 } \\\\ &\mathbf{=}& \mathbf{\sqrt{ 7 }} \\ \hline \end{array}$$

May 3, 2018
#2
+956
+2

Thank you so much for all your help, Heureka!!!

Julius  May 3, 2018