What is the component of 3hat{i} + 4hat{j} al | vedclass

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(D) Let $\vec{a} = 3\hat{i} + 4\hat{j}$ and $\vec{b} = \hat{i} + \hat{j}$.The component of $\vec{a}$ along $\vec{b}$ is given by the formula: $\vec{a}

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$\frac{7}{2}(\hat{i} + \hat{j})$

Vedclass · Answer

(D) Let $\vec{a} = 3\hat{i} + 4\hat{j}$ and $\vec{b} = \hat{i} + \hat{j}$.The component of $\vec{a}$ along $\vec{b}$ is given by the formula: $\vec{a}_{	ext{parallel}} = \left( \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|^2} ight) \vec{b}$.First,calculate the dot product: $\vec{a} \cdot \vec{b} = (3)(1) + (4)(1) = 3 + 4 = 7$.Next,calculate the square of the magnitude of $\vec{b}$: $|\vec{b}|^2 = (1)^2 + (1)^2 = 1 + 1 = 2$.Substitute these values into the formula: $\vec{a}_{	ext{parallel}} = \left( \frac{7}{2} ight) (\hat{i} + \hat{j})$.Thus,the component is $\frac{7}{2}(\hat{i} + \hat{j})$.

What is the component of $3\hat{i} + 4\hat{j}$ along $\hat{i} + \hat{j}$?

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