Question

Write the equation of line through the points A(0,2,1) and B(0,1,9) in Cartesian and vector form














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Answer 1

${ \bold{ \underline{ \underline{Hey \: \: There!}}}}$

${ \sf{ \underline{Equation \: of \: Line \: in \: Vector \: form }}} \\ \\ \implies \: r \: = a + \gamma (b - a)$

Here a = 2j + k and b = j + 8k

And ( b - a) = -j + 7k

Plugging the values , we get the equation →

$\rightarrow \:{ \bold{ r = 2j + k \: + \gamma ( - j + 7k)}}$

${ \sf{ \underline{Equation \: of \: Line \: in \: Cartesian \: form}}} \\ \\ \implies \: \dfrac{x - x_1}{x_2 - x_1} = \: \dfrac{y - y_1}{y_2 - y_1} = \: \dfrac{z - z_1}{z_2 - z_1}</p><p></p><p></p><p></p><p></p><p></p><p>$

Here x¹ ( 0,2,1 ) and x2 ( 0,1,9)

So plugging the values we get the equation →

$\rightarrow \dfrac{x - 0}{ 0} = \dfrac{y - 2}{ - 1} = \dfrac{z - 1}{7}$

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