Q. 125.0( 1 Vote )

# Find the direction cosines of the unit vector perpendicular to the plane + 1 = 0 passing through the origin.

Answer :

The given plane equation is

Now, we calculate the magnitude of the vector.

On dividing both sides of the plane equation by 7, we get

Recall that the equation of the plane in normal form is given by where is a unit vector perpendicular to the plane through the origin.

So, here

This is a unit vector normal to the plane.

Thus, the direction cosines of the unit vector perpendicular to the given plane are.

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