The scalar and vector product of two vectors, and is equal to:
1. -25 &
2. 25 &
3. 0 &
4. -25 &
The magnitude of the resultant of two forces \(A=8\) N and \(B=6\) N acting at a point angle of between them is:
1. \(14\) N
2. \(2\) N
3. \(10\) N
4. \(12\) N
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) | \(\vec A\)| or |\(\vec B\)| is zero. | when either |
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. | \(\vec{A}.\vec{B}\leq0\) |
Three vectors A, B, and C add up to zero. Then:
1. | vector (A×B)×C is not zero unless vectors B and C are parallel. |
2. | vector (A×B).C is not zero unless vectors B and C are parallel. |
3. | if vectors A, B and C define a plane, (A×B)×C is in that plane. |
4. | (A×B).C = |A||B||C| → C2 = A2 + B2 |
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. |