Three vectors \(A,B\) and \(C\) add up to zero. Then:

1.	vector \((A\times B)\times C\) is not zero unless vectors \(B\) and \(C\) are parallel.
2.	vector \((A\times B).C\) is not zero unless vectors \(B\) and \(C\) are parallel.
3.	if vectors \(A,B\) and \(C\) define a plane, \((A\times B)\times C\) is in that plane.
4.	\((A\times B). C= |A||B||C|\rightarrow C^2= A^2+B^2\)

The incorrect statement/s is/are:
1. (b), (d)
2. (a), (c)
3. (b), (c), (d)
4. (a), (b)

It is found that \(|\vec{A}+\vec{B}|=|\vec{A}|\). This necessarily implies:

For two vectors \(\vec A\) and \(\vec B\), |\(\vec A\)+\(\vec B\)|=|\(\vec A\) - \(\vec B\)| is always true when:

Consider the quantities of pressure, power, energy, impulse, gravitational potential, electric charge, temperature, and area. Out of these, the only vector quantities are the following:
1. impulse, pressure, and area
2. impulse and area
3. area and gravitational potential
4. impulse and pressure

The component of a vector \(\vec{r}\) along the X-axis will have maximum value if:

The figure shows the orientation of two vectors \(u\) and \(v\) in the XY plane.
If \(u=a\hat{i}+b\hat{j}\) and \(v=p\hat{i}+q\hat{j}\).

      
Which of the following is correct?

Which one of the following statements is true?

1. A scalar quantity is the one that is conserved in a process.

2. A scalar quantity is one that can never take negative values.

3. A scalar quantity is one that does not vary from one point to another in space.

4. A scalar quantity has the same value for observers with different orientations of the axes.

The vector sum of two forces is perpendicular to their vector difference. Which of the following statements is correct?

If the angle between the two forces increases, the magnitude of their resultant:

1. Decreases

2. Increases

3. Remains unchanged

4. First decreases, then increases