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)
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
If is right-angled at C, then the value of cos (A + B) is:
1. \(0\)
2. \(1\)
3. \(\frac{1}{2}\)
4. \(\frac{\sqrt{3}}{2}\)
Which of the following is not possible?
1. sin \(\theta\) = \(3\over5\)
2. sec \(\theta\) = \(100\)
3. cosec \(\theta\) = \(0.14\)
4. None of the above
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 |
The component of a vector \(r\) along the \(X\)-axis will have the maximum value if:
1. | \(r\) is oriented along the positive \(Y\)-axis |
2. | \(3r\) is oriented along the positive \(X\)-axis |
3. | \(r\) makes an angle of \(45^{\circ}\) with the \(X\)-axis |
4. | \(r\) is along the negative \(Y\)-axis |
If the sum of two unit vectors is also a unit vector, then the magnitude of their difference and angle between the two given unit vectors is:
1. \(\sqrt{3}, 60^{\circ}\)
2. \(\sqrt{3}, 120^{\circ}\)
3. \(\sqrt{2}, 60^{\circ}\)
4. \(\sqrt{2},120^{\circ}\)
Let \(\theta\) be the angle between vectors \(\overrightarrow A\) and \(\overrightarrow {B}\). Which of the following figures correctly represents the angle \(\theta\)?
1. | 2. | ||
3. | 4. |
The dot product of two mutual perpendicular vector is:
1. \(0\)
2. \(1\)
3. \(\infty\)
4. None of the above