The vector overrightarrow{OA} where O is the | vedclass

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(A) The initial vector is $\overrightarrow{OA} = 2\hat{i} + 2\hat{j}$.The magnitude of the vector is $|\overrightarrow{OA}| = \sqrt{2^2 + 2^2} = \sqrt

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$2\sqrt{2}\hat{j}$

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(A) The initial vector is $\overrightarrow{OA} = 2\hat{i} + 2\hat{j}$.The magnitude of the vector is $|\overrightarrow{OA}| = \sqrt{2^2 + 2^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}$.The angle $	heta$ that the vector makes with the positive $x$-axis is given by $	an 	heta = \frac{y}{x} = \frac{2}{2} = 1$,which means $	heta = 45^{\circ}$.When the vector is rotated by $45^{\circ}$ in the anticlockwise direction,the new angle with the positive $x$-axis becomes $45^{\circ} + 45^{\circ} = 90^{\circ}$.$A$ vector with magnitude $2\sqrt{2}$ at an angle of $90^{\circ}$ with the positive $x$-axis lies entirely along the positive $y$-axis.Therefore,the new vector is $2\sqrt{2}\hat{j}$.

The vector $\overrightarrow{OA}$ where $O$ is the origin is given by $\overrightarrow{OA} = 2\hat{i} + 2\hat{j}$. If it is rotated by $45^{\circ}$ in the anticlockwise direction about $O$,what will be the new vector?

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