Question

If the straight line \( \frac{x - a}{1} = \frac{y - b}{2} = \frac{z - 3}{-1} \) passes through \( (-1, 3, 2) \), then the values of \( a \) and \( b \) are, respectively:

• A. 2, -1
• B. 1, 3
• C. -1, -3
• D. -2, 1
• E. -1, 1

Hint:

Use parametric equations to find the coordinates of points on a line and substitute known values to solve for unknowns.

Answer 1

The Correct Option is D

We are given that the line passes through \( (-1, 3, 2) \). 
Using the parametric form of the line: \[ x = a + t, \quad y = b + 2t, \quad z = 3 - t \] Substituting \( (-1, 3, 2) \) into the parametric equations: \[ -1 = a + t, \quad 3 = b + 2t, \quad 2 = 3 - t \] From the third equation, solving for \( t \): \[ t = 1 \] Now substitute \( t = 1 \) into the first two equations: \[ -1 = a + 1 \quad \Rightarrow \quad a = -2 \] \[ 3 = b + 2(1) \quad \Rightarrow \quad b = 1 \]