Question

Direction ratios of a vector parallel to the line \( \frac{x - 1}{2} = -y = \frac{2z + 1}{6} \) are:

• A. \( 2, -1, 6 \)
• B. \( 2, 1, 6 \)
• C. \( 2, 1, 3 \)
• D. \( 2, -1, 3 \)

Hint:

To find direction ratios, express the line equations in parametric form and extract the coefficients of the parameter \( t \).

Answer 1

The Correct Option is D

Step 1: {Write the direction ratios from the given line equation}
The given line is: \[ \frac{x - 1}{2} = -y = \frac{2z + 1}{6}. \] Equating these to a parameter \( t \), we get: \[ x - 1 = 2t, \quad y = -t, \quad 2z + 1 = 6t. \] Step 2: {Find the direction ratios}
From \( x = 2t + 1 \), \( y = -t \), and \( z = 3t - \frac{1}{2} \), the direction ratios of the line are: \[ 2, -1, 3. \] Conclusion: The direction ratios are \( 2, -1, 3 \).