Q. 225.0( 2 Votes )

# Write the equation of a plane which is at a distance of units from the origin and the normal to which is equally inclined to coordinate axes.

Answer :

Given, the plane is at a distance of units form the origin and the normal to the plane is equally inclined with the co - ordinates axis, so, its direction cosines are

We know, for a plane having direction cosines as l, m and n, and p be the distance of the plane from the origin, the equation of the plane is given as, lx + my + nz=p

So, in this problem, the equation of the required equation of the plane is given by,

=15

Hence, the equation of the required plane which is at a distance of units from the origin and the normal to which is equally inclined to co - ordinate axes is

x + y + z=15.

Rate this question :

Find the equation of the plane which contains the line of intersection of the planes

and

and whose intercept on the x-axis is equal to that of on y-axis.

Mathematics - Board PapersFind the coordinates of the point where the line through the points A (3, 4, 1) and B (5, 1, 6) crosses the XY-plane.

Mathematics - Board PapersFind the distance of the point (–1, –5, –10), from the point of intersection of the line and the plane

Mathematics - Board PapersFind the coordinates of the foot of the perpendicular and the perpendicular distance of the point P(3, 2, 1) from the plane 2x - y + z + 1 = 0. Find also, the image of the point in the plane.

Mathematics - Board PapersFind the Cartesian equation of the plane passing through the points A(0, 0, 0) and B(3, - 1, 2) and parallel to the line

Mathematics - Board PapersFind the coordinate of the point P where the line through and crosses the plane passing through three points and Also, find the ratio in which P divides the line segment AB.

Mathematics - Board Papers