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Sagot :
If the vector is pointing in the opposite direction of [-4,3], we can say it is pointing in the same direction of the vector [4,-3]. We just flipped the direction of the vector by changing the sign of the components.
We have now a vector that is pointing in the same direction of the vector we are looking for. Let's find the length of that vector to see how much it has to be scaled, or if it does not need to be scaled.
The length of the vector is calculated as the square root of the sum of the square of its components:
[tex]\text{Length}=\sqrt[]{x^2+y^2}[/tex]Then, the length of the vector is:
[tex]\begin{gathered} \text{Length}=\sqrt[]{4^2+(-3)^2}=\sqrt[]{16+9}=\sqrt[]{25} \\ \\ \text{Length}=5 \end{gathered}[/tex]Then the length of the vector [4,-3], which is pointing opposite to the vector [-4,3], happens to have a length of 5, then, that is the vector we were looking for. There is no need to scale it.
Then, the components of the vector are 4 and -3. [4,-3]
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