Question

The line \( x = 1 + 5\mu, y = -5 + \mu, z = -6 - 3\mu \) passes through which of the following points?

• A. \( (1, -5, 6) \)
• B. \( (1, 5, 6) \)
• C. \( (1, -5, -6) \)
• D. \( (-1, -5, 6) \)

Hint:

To find a point on a parametric line, substitute the value of the parameter into the parametric equations for \( x \), \( y \), and \( z \).

Answer 1

The Correct Option is C

Step 1: Substituting \( \mu = 0 \) into the parametric equations. To find the point through which the line passes, substitute \( \mu = 0 \) into the parametric equations: \[ x = 1 + 5(0) = 1, \quad y = -5 + (0) = -5, \quad z = -6 - 3(0) = -6 \] Thus, the point is \( (1, -5, -6) \).