Find the component of vector vec{P} = 2 hat{i | vedclass

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(C) The component of a vector $\vec{P}$ along the direction of another vector $\vec{Q}$ is given by the projection formula: $	ext{Component} = \vec{P

Vedclass · Accepted Answer

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

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(C) The component of a vector $\vec{P}$ along the direction of another vector $\vec{Q}$ is given by the projection formula: $	ext{Component} = \vec{P} \cdot \hat{Q} = \vec{P} \cdot \frac{\vec{Q}}{|\vec{Q}|}$.Given $\vec{P} = 2 \hat{i} + 3 \hat{j}$ and $\vec{Q} = \hat{i} + \hat{j}$.First, calculate the magnitude of vector $\vec{Q}$:$|\vec{Q}| = \sqrt{1^2 + 1^2} = \sqrt{2}$.Now, calculate the dot product $\vec{P} \cdot \vec{Q}$:$\vec{P} \cdot \vec{Q} = (2 \hat{i} + 3 \hat{j}) \cdot (\hat{i} + \hat{j}) = (2 	imes 1) + (3 	imes 1) = 2 + 3 = 5$.Finally, the component of $\vec{P}$ along $\vec{Q}$ is:$\frac{\vec{P} \cdot \vec{Q}}{|\vec{Q}|} = \frac{5}{\sqrt{2}}$.

Find the component of vector $\vec{P} = 2 \hat{i} + 3 \hat{j}$ along the direction of vector $\vec{Q} = \hat{i} + \hat{j}$.

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