The vector component of vec{a} = 2hat{i} + 3h | vedclass

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(C) The vector component of $\vec{a}$ in the direction of $\vec{b}$ is given by the projection vector formula: $\vec{a}_{	ext{proj}} = \left( \frac{\

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$\frac{5}{2}(\hat{i} + \hat{j})$

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(C) The vector component of $\vec{a}$ in the direction of $\vec{b}$ is given by the projection vector formula: $\vec{a}_{	ext{proj}} = \left( \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|^2} ight) \vec{b}$.Given $\vec{a} = 2\hat{i} + 3\hat{j}$ and $\vec{b} = \hat{i} + \hat{j}$.First,calculate the dot product: $\vec{a} \cdot \vec{b} = (2)(1) + (3)(1) = 2 + 3 = 5$.Next,calculate the square of the magnitude of $\vec{b}$: $|\vec{b}|^2 = (1)^2 + (1)^2 = 2$.Now,substitute these values into the formula:$\vec{a}_{	ext{proj}} = \left( \frac{5}{2} ight) (\hat{i} + \hat{j})$.Thus,the vector component is $\frac{5}{2}(\hat{i} + \hat{j})$.

The vector component of $\vec{a} = 2\hat{i} + 3\hat{j}$ along the direction of vector $\vec{b} = (\hat{i} + \hat{j})$ is:

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