Home » Blog » Find the Cartesian equation of the plane parallel to given vectors with given intercept

Find the Cartesian equation of the plane parallel to given vectors with given intercept

by RoRi

Consider the plane which is parallel to both of the vector \mathbf{i} + \mathbf{j} and \mathbf{j} + \mathbf{k} and intersects the x-axis at the point (2,0,0). Find the Cartesian equation of this plane.

Since M contains the point (2,0,0) and is parallel to (1,1,0) and (0,1,1) we have

    \[ M = \{ (2,0,0) + s(1,1,0) + t(0,1,1) \}. \]

Thus, the Cartesian equations for M are

    \[ x = 2s, \qquad y = s + t, \qquad z = t. \]

Hence,

    \[ x - y + z = 2. \]

Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):