If the cartesian equations of a line are write the vector equation for the line.[CBSE 2014]

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 .