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  4. The scalar product of two vectors vecA =2 hati+2 hatj- hatk and vecB = - hatj+ hatk, is given by

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Q. The scalar product of two vectors $ \vec{A} =2\hat{i}+2\hat{j}-\hat{k} $ and $\vec{B} = -\hat{j}+\hat{k}, $ is given by

J & K CETJ & K CET 2013Work, Energy and Power

Solution:

Given, $A=2 \hat{i}+2 \hat{j}-\hat{k}$ and $B=-\hat{j}+\hat{k}$
Scalar product $A \cdot B=(2 \hat{i}+2 \hat{j}-\hat{k}) \cdot(-\hat{j}+\hat{k})$
Using $\hat{i} \cdot \hat{i}=1, \hat{j} \cdot \hat{j}=1, \hat{k} \cdot \hat{k}=1=1$
we have $A \cdot B=-2-1=-3$