The equation of given plane is or ...(1) The equation of given line is ...(2) Now line (2) passes through the point (2, -3, 5), With position vector and is parallel to the vector Now plane (1) passes through the point with position vector if i.e. if (2) (-3) + (-3) (-1) + (5) (1) = 2 i.e. if 2 = 2, which is true Now, is a vector normal to the plane (1). It will be perpendicular to the line (2) if it is perpendicular i.e. if (–3) (1) + (– 1) (– 1) + (1) (2) = 0 i.e. if –3 + 1+ 2 = 0 i.e. if 0 = 0, which is true ∴ line (2) lies in plane (1).
83 Views
Advertisement
296.Show that the line whose vector equation is lies in the plane whose vector equation is
78 Views
297.Find the equations of the line passing through (1, – 2, 3) and parallel to the planes x – y + 2 z = 5 and 3 x + 2y – z = 6.
91 Views
Long Answer Type
298.Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes
73 Views
Advertisement
299.Find the vector equation of the line passing through the point (1, 2, – 4) and perpendicular to the lines:
105 Views
300.Find the equation of the plane containing the line and the point (0, 6, 0).