P and Q are two non-zero vectors inclined to | vedclass

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(C) Let two vectors $P$ and $Q$ be represented as shown in the figure.Here,$Q_P$ is the component of vector $Q$ in the direction of vector $P$.From th

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$\frac{P \cdot Q}{P}$

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(C) Let two vectors $P$ and $Q$ be represented as shown in the figure.Here,$Q_P$ is the component of vector $Q$ in the direction of vector $P$.From the right-angled triangle formed by the projection of $Q$ onto $P$,we have:$\cos 	heta = \frac{Q_P}{Q}$$\Rightarrow Q_P = Q \cos 	heta$We know that the dot product of two vectors is given by $P \cdot Q = PQ \cos 	heta$.Therefore,$\cos 	heta = \frac{P \cdot Q}{PQ}$.Substituting this into the expression for $Q_P$:$Q_P = Q \left( \frac{P \cdot Q}{PQ} ight)$$Q_P = \frac{P \cdot Q}{P}$Thus,the component of $Q$ in the direction of $P$ is $\frac{P \cdot Q}{P}$.

$P$ and $Q$ are two non-zero vectors inclined to each other at an angle $\theta$. The component of $Q$ in the direction of $P$ is:

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