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1.Calculate the unit vector for v = <3, 4>

2.Find a vector with length 10 in the same direction of v.

 May 19, 2020
 #1
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1.

Calculate the unit vector for v = <3, 4>

\(\mathbf{v_{\text{unit}}} = < \dfrac{3} { \sqrt{3^2+4^2} } ,\ \dfrac{4}{\sqrt{3^2+4^2}} > \\ \mathbf{v_{\text{unit}}} = < \dfrac{3} {5} ,\ \dfrac{4}{5} >\)

 

2.

Find a vector with length 10 in the same direction of v.

\(\begin{array}{|rcll|} \hline && 10\mathbf{v_{\text{unit}}} \\ &=& 10*< \dfrac{3} {5} ,\ \dfrac{4}{5} > \\ &=& < \dfrac{10*3} {5} ,\ \dfrac{10*4}{5} > \\ &=& < \dfrac{30} {5} ,\ \dfrac{40}{5} > \\ &=& \mathbf{ < 6 ,\ 8 > } \\ \hline \end{array}\)

 

laugh

 May 19, 2020
edited by heureka  May 19, 2020

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