Zero Vector

Q. Given a + b + c + d = 0, which of the following statements are correct : (a) a, b, c, and d must each be a null vector, (b) The magnitude of (a + c) equals the magnitude of ( b + d), (c) The magnitude of a can never be greater than the sum of the magnitudes of b, c, and d, (d) b + c must lie in the plane of a and d if a and d are not collinear, and in the line of a and d, if they are collinear ?

Q. Three forces $\overrightarrow{F_1}=(3\hat{i}+2\hat{j}-\hat{k})N,\overrightarrow{F_2}=(3\hat{i}+4\hat{j}-5\hat{k})N$ and $\overrightarrow{F_3}=A(\hat{i}+\hat{j}-\hat{k})N$ act simultaneously on a particle. In order that the particle remains in equilibrium, the value of A should be

1. -6
2. 6
3. 9
4. -9

Q. Which of the following is a null vector?

1. Velocity vector of a body moving in a circle with a uniform speed
2. Velocity vector of a body moving in a straight line with a uniform speed
3. Position vector of the origin of a rectangular coordinate system
4. Displacement vector of a stationary object
   

Q.

wrong statement ?

a)vectors are having both magnitude and direction

b)a unit vector has no dimention and unit

c) a null vector is having specific direction

d)a unit vector is used to specify only direction

e)vector addition is commutative

Q.

The dot product of mutually perpendicular vectors is always:

1. Zero

2. Null vector

3. Vector

4. Non-Zero Scalar

Q. A metal sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The forces acting on the sphere are shown in the second diagram. Which of the following statements is wrong

1. P = W tan $\theta$
2. T= P+W
3. $T^2$ = $P^2$ + $W^2$
4. none of these

Q. Direction of zero vector is

1. Towards $x-$axis
2. Towards origin
3. Indeterminate
4. Away from the origin

Q. The magnitude of the vector product of two vectors $\left|\overrightarrow{A}\right|$ and $\left|\overrightarrow{B}\right|$ may be
(a) greater than AB
(b) equal to AB
(c) less than AB
(d) equal to zero.

Q.

What does the direction of zero vector mean ?

Q. Is it true to say unit vector has no unit and direction.

Q. if a object is vector then it should have the magnitude, the direction, and should obey the laws of vector , but if the object has magnitude and obey the laws of vector but does not have direction then the object will still be vector or some other quantity?

Q.

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ lie in a plane, another vector $\overrightarrow{C}$ lies outside this plane, then the resultant of these three vectors i.e., $\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}$

1. Can be zero

2. Cannot be zero

3. Lies in the plane containing $\overrightarrow{A}+\overrightarrow{B}$

4. Lies in the plane containing $\overrightarrow{C}$