A line passes through the point $(x_1,y_1,z_1)$ and has direction ratios $(a,b,c)$. Which of the following is its symmetric form?
A$\dfrac{x-x_1}{a}=\dfrac{y-y_1}{b}=\dfrac{z-z_1}{c}$
B$\dfrac{x+x_1}{a}=\dfrac{y+y_1}{b}=\dfrac{z+z_1}{c}$
C$\dfrac{x-x_1}{x}=\dfrac{y-y_1}{y}=\dfrac{z-z_1}{z}$
D$ax+by+cz=1$
Answer & Solution
Correct answer: A. $\dfrac{x-x_1}{a}=\dfrac{y-y_1}{b}=\dfrac{z-z_1}{c}$
For a line through $(x_1,y_1,z_1)$ with direction ratios $(a,b,c)$, the standard symmetric form is $\dfrac{x-x_1}{a}=\dfrac{y-y_1}{b}=\dfrac{z-z_1}{c}$. The other options do not represent the general equation of such a line.
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