First slide

Equation of line in Straight lines

Question

If O is the origin and $P (x_{1}, y_{1}), Q (x_{2}, y_{2})$ are two points, then $O P . O Q \cos ∠ P O Q$

Easy

A

$x_{1} x_{2} + y / 1 y_{2}$
B

$x_{1} y_{2} + x_{2} y_{1}$
C

$|\begin{array}{llll} x_{1} y_{2} - x_{2} y_{1} \end{array}|$
D

none of these

Solution

Using cosine formula in $∆ P O Q$ we have
$\begin{array}{l} P Q^{2} = O P^{2} + O Q^{2} - 2 O P \times O Q \cos ∠ P O Q \\ \Rightarrow {(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2} = x_{1}^{2} + y_{1}^{2} + x_{2}^{2} + y_{2}^{2} - 2 O P \times O Q \cos ∠ P O Q \end{array}$
$\Rightarrow O P \cdot O Q \cos ∠ P O Q = x_{1} x_{2} + y_{1} y_{2}$

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