The direction ratios of a line parallel to the line whose equations are \( 6x-2=3y+1=2z-2 \) are:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1, 2, 3
Let each expression be equal to a parameter \( k \):
\( \displaystyle 6x-2=3y+1=2z-2=k\ \)
\( \displaystyle \Rightarrow\ x=\frac{k+2}{6},\ \ y=\frac{k-1}{3},\ \ z=\frac{k+2}{2} \)
The coefficients of \( k \), namely \( \frac{1}{6},\ \frac{1}{3},\ \frac{1}{2} \), are the direction ratios of the line.
Multiplying by 6 to clear the fractions gives \( 1,\ 2,\ 3 \).