Question

Which of the following cannot be the direction ratios of the straight line \(\frac{x - 3}{2} = \frac{2 - y}{3} = \frac{z + 4}{-1}\)?

• A. \(2, -3, -1\)
• B. \(-2, 3, 1\)
• C. \(2, 3, -1\)
• D. \(6, -9, -3\)

Answer 1

The Correct Option is C

The direction ratios of a straight line are the coefficients of x, y, and z in the parametric form of the line.

The given equation of the line is:

This can be rewritten in parametric form as:

x = 3 + 2t, y = 2 - 3t, z = -4 - t.

Thus, the direction ratios are 2, -3, -1.

Now, check each option:

Option (1) 2, -3, -1 is correct since it matches the direction ratios.

Option (2) -2, 3, 1 is a negative multiple of the correct direction ratios, so it is valid.

Option (3) 2, 3, -1 does not match the direction ratios, as the second direction ratio should be negative.

Option (4) 6, -9, -3 is a positive multiple of the direction ratios, so this is valid.

Thus, the correct answer is:

2, -3, -1.