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Standard Equation of Ellipse

If a straight...

Question

If a straight line passes through the two given points, $P_{1} (x_{1}, y_{1})$ , and $P_{2} (x_{2}, y_{2})$ , then the vector equation of the line will be

A

\to r = {\to r}_{1} + t_{1}

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B

\to r = {\to r}_{1} + t ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ P_{1} P 2

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C

\to r = {\to r}_{1} + t ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ P_{1} - P 2

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D

\to r = {\to r}_{1} + t ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ P_{1} + P 2

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Solution

The correct option is B $\to r = {\to r}_{1} + t ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ P_{1} P 2$
from diagram position vector of line is $O P_{1} =_{1}$
line passing through $P_{1}, P_{2}$
so normal vector
$\to n = \to P_{1} P_{2} = O P_{2} - O P_{1} = P_{1} P_{2}$
eq of line
$\to r =_{1} + t \to P_{1} P_{2}$

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