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
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)
D.
(2, - 3, 4)
Let the foot of the perpendicular in the 2x - 3y + 4z = 29 be P.
So, the point satisfy the given plane.
Since, OF is perpendicular to the given plane. Therefore, normal to the plane is parallel to OF.
On putting the value of in Eq.(i), we get
2(2k) - 3(- 3k) + 4(4k) = 29
Hence, foot of perpendicular is (2, - 3, 4).