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Work Energy And Power

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1. Scalar Product

  • Also called dot product
  • \(\overrightarrow{A}.\overrightarrow{B}=AB\cos (\theta )\)
  • \(\overrightarrow{A}.\overrightarrow{B}=\overrightarrow{B}\overrightarrow{.A}\)
  • \(\overrightarrow{A}.\left( \overrightarrow{B}+\overrightarrow{C} \right)=\overrightarrow{A}.\overrightarrow{B}+\overrightarrow{A}.\overrightarrow{C}\)
  • \(\hat{i}.\hat{i}=\hat{j}.\hat{j}=\hat{k}.\hat{k}=1\)
  • \(\hat{i}.\hat{j}=\hat{j}.\hat{k}=\hat{k}.\hat{i}=0\)
  • \(\left( {{A}_{X}}\hat{j}+{{A}_{Y}}\hat{j}+{{A}_{2}}\hat{k} \right).({{B}_{X}}\hat{i}+{{B}_{Y}}\hat{j}+{{B}_{2}}\hat{k})\)

            \(={{A}_{X}}{{B}_{X}}+{{A}_{Y}}{{B}_{Y}}={{A}_{Z}}{{B}_{Z}}\)

 

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