The component of a vector P=3 hat{i}+4 hat{j} | vedclass

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(B) Given vector $P = 3 \hat{i} + 4 \hat{j}$.Let the direction vector be $Q = \hat{i} + 2 \hat{j}$.The component of vector $P$ along the direction of

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$\frac{11}{\sqrt{5}}$

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(B) Given vector $P = 3 \hat{i} + 4 \hat{j}$.Let the direction vector be $Q = \hat{i} + 2 \hat{j}$.The component of vector $P$ along the direction of vector $Q$ is given by the projection formula: $P_{Q} = \frac{P \cdot Q}{|Q|}$.First,calculate the dot product $P \cdot Q = (3 \hat{i} + 4 \hat{j}) \cdot (\hat{i} + 2 \hat{j}) = (3 	imes 1) + (4 	imes 2) = 3 + 8 = 11$.Next,calculate the magnitude of vector $Q$: $|Q| = \sqrt{1^2 + 2^2} = \sqrt{1 + 4} = \sqrt{5}$.Therefore,the component is $\frac{P \cdot Q}{|Q|} = \frac{11}{\sqrt{5}}$.

The component of a vector $P=3 \hat{i}+4 \hat{j}$ along the direction $(\hat{i}+2 \hat{j})$ is

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