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

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Question

(A) The component of vector $\vec{A}$ along vector $\vec{B}$ is given by the projection formula: $	ext{Component} = \frac{\vec{A} \cdot \vec{B}}{|\ve

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The component of vector $\vec{A}$ along vector $\vec{B}$ is given by the projection formula: $	ext{Component} = \frac{\vec{A} \cdot \vec{B}}{|\vec{B}|}$.Given $\vec{A} = 2\hat{i} + 3\hat{j}$ and $\vec{B} = \hat{i} + \hat{j}$.The dot product $\vec{A} \cdot \vec{B} = (2)(1) + (3)(1) = 2 + 3 = 5$.The magnitude of vector $\vec{B}$ is $|\vec{B}| = \sqrt{1^2 + 1^2} = \sqrt{2}$.Therefore,the component 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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