If a, b and c are three non-zero vectors such that each one of them being perpendicular to the sum of the other two vectors, then the value of is
2
Let u, v and w be vectors such that u + v + w = 0. If , then u - v + v · w + w · u is equal to
0
- 25
25
50
Equation of the plane through the mid-point of the line segment joining the points P(4, 5, - 10), Q(- 1, 2, 1) and perpendicular to PQ is
The angle between the straight lines and x = 3r + 2; y = - 2r - 1; z = 2, where r is a parameter, is
Equation of the line through the point (2, 3, 1) and parallel to the line of intersection of the planes x - 2y - z + 5 = 0 and x + y + 3z = 6 is
A.
Given equation of planes are,
x - 2y - z + 5 = 0
and x + y + 3z = 6
Firstly, determine the intersection lines of two planes.
Let the DR's of intersection line are a, b and c.
Since, the normal to the given planes are perpendicular to the intersecting line.
Since, the required line is passing through (2, 3, 1) and parallel to the line of intersection.
Foot of the perpendicular drawn from the origin to the plane 2x - 3y + 4z = 29 is
(5, - 1, 4)
(7, - 1, 3)
(5, - 2, 3)
(2, - 3, 4)