If a vector having magnitude of 5 units, makes equal angle with each of the three mutually perpendicular axes,then the sum of the magnitude of the projections on each of the axis is
A force of 78 grams acts at the point (2,3,5). The direction ratios of the line of action being 2,2,1 . The magnitude of its moment about the line joining the origin to the point (12,3,4) is
The value of m for which volume of the parallelepiped is 4 cubic units whose three edges are represented by a = mi + j + k, b = i – j + k, c = i + 2j –k is
A man starts at the origin O and walks a distance of 3 units in the north-
east direction and then walks a distance of 4 units in the north-west
direction to reach the point P. then →OP is equal to
How much work does it take to slide a crate for a distance of 25m along a loading
dock by pulling on it with a 180 N force where the dock is at an angle of 45°
from the horizontal?
Let →a=2ˆi+ˆj+2ˆk , →b=ˆi−ˆj+2ˆk and →c=ˆi+ˆj−2ˆk are are three vectors. Then, a vector in the plane of →a and →c whose projection on →b is of magnitude 1√6 is
A bird is flying in a straight line with velocity vector 10i+6j+k, measured in km/hr. If the starting point is (1,2,3), how much time does it to take to reach a point in space that is 13m high from the ground?
Two forces F1 and F2 are used to pull a car, which met an accident. The angle between the two forces is θ . Find the values of θ for which the resultant force
is equal to
Forces of magnitude 5, 3, 1 units act in the directions
6i + 2j + 3k, 3i - 2j + 6k, 2i - 3j - 6k respectively on a particle which is displaced from the
point (2, −1, −3) to (5, −1, 1). The total work done by the force is
If a, b, c are three non-zero vectors with no two of
which are collinear, a + 2b is collinear with c and b + 3c is collinear with a , then | a + 2b + 6c | will
be equal to
If →a and →b are vectors in space, given by →a=ˆi−2ˆj√5 and →b=2ˆi+ˆj+3ˆk√14, then the value of(2\vec{a} + \vec{b}).[(\vec{a} × \vec{b}) × (\vec{a} – 2\vec{b})] is
Let \vec{A} = 2\hat{i} + \hat{j} – 2\hat{k} and \vec{B} = \hat{i} + \hat{j}, If \vec{C} is a vector such that |\vec{C} – \vec{A}| = 3 and the angle between A × B and C is {30^{\circ}}, then |(\vec{A} × \vec{B}) × \vec{C}| = 3 then the value of \vec{A}.\vec{C} is equal to