Practice Lines in 3D in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Lines in three-dimensional space described using parametric equations x = x_0 + at, y = y_0 + bt, z = z_0 + ct, or symmetric form \frac{x - x_0}{a} = \frac{y - y_0}{b} = \frac{z - z_0}{c}, where (x_0, y_0, z_0) is a point on the line and \langle a, b, c \rangle is the direction vector.
In 2D, a line is defined by a slope and a point (y = mx + b). In 3D, slope doesn't work—there's no single number for direction in space. Instead, you specify a starting point and a direction vector (an arrow pointing along the line). The parameter t acts like a slider: at t = 0 you're at the starting point, and as t increases or decreases, you slide along the line in the direction of the vector.