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

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Question

(A) The component of a vector $\vec{A}$ along the direction of a vector $\vec{B}$ is given by the scalar projection multiplied by the unit vector of $

Vedclass · Accepted Answer

$\frac{5}{\sqrt{2}}$

Vedclass · Answer

(A) The component of a vector $\vec{A}$ along the direction of a vector $\vec{B}$ is given by the scalar projection multiplied by the unit vector of $\vec{B}$,or simply the scalar projection if only the magnitude is asked. The question asks for the component (magnitude) of $\vec{A}$ along $\vec{B}$.Given $\vec{A} = 2\hat{i} + 3\hat{j}$ and $\vec{B} = \hat{i} + \hat{j}$.The scalar projection of $\vec{A}$ along $\vec{B}$ is given by $\frac{\vec{A} \cdot \vec{B}}{|\vec{B}|}$.Calculate the dot product: $\vec{A} \cdot \vec{B} = (2)(1) + (3)(1) = 2 + 3 = 5$.Calculate the magnitude of $\vec{B}$: $|\vec{B}| = \sqrt{1^2 + 1^2} = \sqrt{2}$.Therefore,the component of $\vec{A}$ along $\vec{B}$ is $\frac{5}{\sqrt{2}}$.

The component of vector $\vec{A} = 2\hat{i} + 3\hat{j}$ along the vector $\vec{B} = \hat{i} + \hat{j}$ is:

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