Two vectors vec{A} = 3hat{i} + hat{j} and vec | vedclass

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(D) The component of vector $\vec{A}$ along vector $\vec{B}$ is given by the formula: $\vec{A}_{	ext{along } B} = \left( \frac{\vec{A} \cdot \vec{B}}

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$\frac{1}{5}(\hat{j} + 2\hat{k})$

Vedclass · Answer

(D) The component of vector $\vec{A}$ along vector $\vec{B}$ is given by the formula: $\vec{A}_{	ext{along } B} = \left( \frac{\vec{A} \cdot \vec{B}}{|\vec{B}|} ight) \hat{B} = \left( \frac{\vec{A} \cdot \vec{B}}{|\vec{B}|^2} ight) \vec{B}$.First,calculate the dot product $\vec{A} \cdot \vec{B} = (3\hat{i} + \hat{j}) \cdot (0\hat{i} + 1\hat{j} + 2\hat{k}) = (3)(0) + (1)(1) + (0)(2) = 1$.Next,calculate the square of the magnitude of $\vec{B}$: $|\vec{B}|^2 = (0)^2 + (1)^2 + (2)^2 = 1 + 4 = 5$.Now,substitute these values into the formula: $\vec{A}_{	ext{along } B} = \frac{1}{5} (\hat{j} + 2\hat{k})$.Thus,the correct option is $D$.

Two vectors $\vec{A} = 3\hat{i} + \hat{j}$ and $\vec{B} = \hat{j} + 2\hat{k}$ are given. Find the component of $\vec{A}$ along $\vec{B}$ in vector form.

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