Question

find a vector equation and parametric equations for the line. (use the parameter t.) the line through the point (5, 2.5, 3.1) and parallel to the vector 4i 3j − k

Answer 1

The line we want is given by the vector equation

L(t) = (4i + 3j - k) t + (5i + 2.5j + 3.1k)

L(t) = (4t + 5) i + (3t + 2.5) j + (-t + 3.1) k

As parametric equations, we write

x(t) = 4t + 5

y(t) = 3t + 2.5

z(t) = -t + 3.1