If the equation of a line is $x = ay + b, z = cy + d$, then find the direction ratios of the line and a point on the line.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Direction Ratios: $(a, 1, c)$; Point: $(b, 0, d)$ ##
$x = ay + b ⇒\frac{x - b}{a} = y$
$z = cy + d ⇒\frac{z - d}{c} = y$
$∴$ Equation of the line:
$\frac{x - b}{a} = \frac{y - 0}{1} = \frac{z - d}{c}$
$\textbf{Direction ratios of the line}: (a, 1, c)$
$\textbf{Point on the line}:(b, 0, d)$