The velocity of a boat X relative to a boat Y is and that of Y relative to another boat Z is where are the velocity of k not per hour, east and north respectively. Then the velocity is :
knot/h
knot/h
knot/h
Two vectors of equal magnitude 5 originating from a point and directs respectively towards north-east and north-west. Then the magnitude of is :
The shortest distance from the point (1, 2, - 1) to the surface of the sphere x2 + y2 + z2 = 24 is :
unit
unit
2 sq unit
The equation of the plane which bisects the line joining (2, 3, 4) and (6, 7, 8) is :
x - y - z - 15 = 0
x - y - z - 15 = 0
x + y + z - 15 = 0
x + y + z + 15 = 0
If are are the three vectors mutually perpendicular to each other and , then is equal to
0
- 24
3600
- 215
A unit vector coplanar with , and perpendicular to is :
A.
Forces acting on a particle have magnitude 5, 3 and 1 unit and act in the direction of the vectors respectively. They remain constant while the particle is displaced from the point A (2, - 1, - 3) to B (5, - 1, 1). The work done is :
11 unit
33 unit
10 unit
30 unit
The equation of the plane through the point (1, 2, 3), (- 1, 4, 2) and (3, 1, 1) is :
5x + y + 12z - 23 = 0
5x + 6y + 2z - 23 = 0
x + 6y + 2z - 13 = 0
x + y + z - 13 = 0