Question

Find symmetric equations for the line that passes through the point (1, -4, 6) and is parallel to the vector( -1, 3, -3) = x-1/-1 = y+4/3 = z-6/-3

Answer 1

The symmetric equations for the line passing through (1, -4, 6) and parallel to the vector (-1, 3, -3) are (x - 1) / -1 = (y + 4) / 3 = (z - 6) / -3.

Step-by-step explanation:

The equation of the line can be found using the point-slope form:

Equation: (x - x1) / a = (y - y1) / b = (z - z1) / c

Given that the point (1, -4, 6) lies on the line, we can substitute the values into the equation:

Equation: (x - 1) / a = (y + 4) / b = (z - 6) / c

Since the line is parallel to the vector (-1, 3, -3), the direction ratios are equal to the direction ratios of the vector. Therefore, a = -1, b = 3, and c = -3.

The symmetric equations for the line are:
Equation 1: (x - 1) / -1 = (y + 4) / 3 = (z - 6) / -3

Equation 2: (x - 1) / -1 = (y + 4) / 3

Equation 3: (x - 1) / -1 = (z - 6) / -3