If the cartesian equations of a line are write the vector equation for the line.

Vector equation for the line is given by

Where is the point on line and is the direction of lithe ne and λ is any constant

Given the cartesian form of a line

Comparing with a standard cartesian form of the equation

Where the point on line is (a₁, a₂, a₃) and (b₁, b₂, b₃) is direction of the line

(a₁, a₂, a₃) = (3, -4, 3) and (b₁, b₂, b₃) = (-5, 7, 2)

Hence and

The vector equation of the line is .