The value of the unit vector, which is perpendicular to both A = \(\hat{i} + 2\hat{j} + 3 \hat{k}\) and B = \(\hat{i} - 2\hat{j} - 3 \hat{k}\) :
1.
2.
3.
4.
The area of a blot of ink, A, is growing such that after t seconds, \(A=3t^2+\frac{t}{5}+7~m^2\). Then the rate of increase in the area at t= 5s will be :
1. 30.1 m2/s
2. 30.2 m2/s
3. 30.3 m2/s
4. 30.4 m2/s
The current in a circuit is defined as . The charge (q) flowing through a circuit, as a function of time (t), is given by . The minimum charge flows through the circuit at:
1. t=4 sec
2. t=2 sec
3. t= 6 sec
4. t=3 sec
If a vector is inclined at angles, with x, y, and z-axis respectively, then the value of is equal to
1. 0
2. 1
3. 2
4.
If are two vectors inclined to each other at an angle , then the component of perpendicular to and lying in the plane containing will be:
1.
2.
3.
4.
If and = , then
1.
2.
3. is antiparallel to
4. is inclined to at an angle of 45
Two forces of the same magnitude are acting on a body in the East and North directions, respectively. If the body remains in equilibrium, then the third force should be applied in the direction of:
1. North-East
2. North-West
3. South-West
4. South-East
Given are two vectors, and . What should be the value of c so that vector would become parallel to each other?
1. 1
2. 2
3. 3
4. 4
A block of weight W is supported by two strings inclined at 60° and 30° to the vertical. The tensions in the strings are as shown. If these tensions are to be determined in terms of W using the triangle law of forces, which of these triangles should you draw? (block is in equilibrium) :-
1. | 2. | ||
3. | 4. |
The magnitude of the resultant of two vectors of magnitude 3 units and 4 units is 1 unit. What is the value of their dot product?
1. –12 units
2. –7 units
3. –1 unit
4. 0