Question

Q.8 Point A(1,2,3), B(4,k.4) and C(-2,4,2) are collinear then find the value of k.

fa A(1,2,3), B(4,k.4)3tR C (-2,4,2)?​

Answer 1

$\textbf{Given:}$

$\textsf{Points A(1,2,3), B(4,k,4),C(-2,4,2) are collinear}$

$\textbf{To find:}$

$\textsf{The value of k}$

$\textbf{Solution:}$

$\textsf{The equation of the line joining A(1,2,3) and B(4,k,4) is}$

$\mathsf{\dfrac{x-x_1}{x_2-x_1}=\dfrac{y-y_1}{y_2-y_1}=\dfrac{z-z_1}{z_2-z_1}}$

$\implies\mathsf{\dfrac{x-1}{4-1}=\dfrac{y-2}{k-2}=\dfrac{z-3}{4-3}}$

$\implies\mathsf{\dfrac{x-1}{3}=\dfrac{y-2}{k-2}=\dfrac{z-3}{1}}$

$\textsf{Since A,B,C are collinear, C lies on}$

$\textsf{the line joining A and B}$

$\implies\mathsf{\dfrac{-2-1}{3}=\dfrac{4-2}{k-2}=\dfrac{2-3}{1}}$

$\implies\mathsf{\dfrac{-3}{3}=\dfrac{2}{k-2}=\dfrac{-1}{1}}$

$\implies\mathsf{-1=\dfrac{2}{k-2}=-1}$

$\implies\mathsf{\dfrac{2}{k-2}=-1}$

$\implies\mathsf{2=-(k-2)}$

$\implies\mathsf{2=-k+2}$

$\implies\boxed{\mathsf{k=0}}$

$\textbf{Find more:}$

If the points (x y -3) (2 0 -1) and (4 2 3) lie on a straight line then what are the values of x and y respectively?​

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