Q. No.The angle between \(\mathrm{A}=\hat{\mathbf{i}}+\hat{\mathbf{j}}\) and \(\mathrm{B}=\hat{\mathbf{i}}-\hat{\mathbf{j}}\) is:
1. \(45^{\circ} \)
2. \(90^{\circ} \)
3. \(-45^{\circ} \)
4. \(180^{\circ}\)
For two vectors \(\vec A\) and \(\vec B\), |\(\vec A\)+\(\vec B\)|=|\(\vec A\) - \(\vec B\)| is always true when:
| (a) | |\(\vec A\)| = |\(\vec B\)| ≠ \(0\) |
| (b) | \(\vec A\perp\vec B\) |
| (c) | |\(\vec A\)| = |\(\vec B\)| ≠ \(0\) and \(\vec A\) and \(\vec B\) are parallel or antiparallel. |
| (d) | when either |\(\vec A\)| or |\(\vec B\)| is zero. |
Choose the correct option:
1. (a), (d)
2. (b), (c)
3. (b), (d)
4. (a), (b)
It is found that \(|\vec{A}+\vec{B}|=|\vec{A}|\). This necessarily implies:
| 1. | \(\vec{B}=0\) |
| 2. | \(\vec{A},\) \(\vec{B}\) are antiparallel |
| 3. | \(\vec{A}\) and \(\vec{B}\) are perpendicular |
| 4. | \(\vec{A}.\vec{B}\leq0\) |
| 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)
Consider the quantities of pressure, power, energy, impulse, gravitational potential, electric charge, temperature, and area. Out of these, the only vector quantities are:
| 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:
| 1. | \(\vec{r}\) is along the positive Y-axis. |
| 2. | \(\vec{r}\) is along the positive X-axis. |
| 3. | \(\vec{r}\) makes an angle of \(45^\circ\) with the X-axis. |
| 4. | \(\vec{r}\) is along the negative Y-axis. |
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?
| 1. | \(a\) and \(p\) are positive while \(b\) and \(q\) are negative. |
| 2. | \(a,\) \(p\) and \(b\) are positive while \(q\) is negative. |
| 3. | \(a,\) \(q\) and \(b\) are positive while \(p\) is negative. |
| 4. | \(a,\) \(b,\) \(p\) and \(q\) are all positive. |
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. In that case, the forces:
| 1. | are not equal to each other in magnitude. |
| 2. | cannot be predicted. |
| 3. | are equal to each other. |
| 4. | are equal to each other in magnitude. |
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
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