\(\overrightarrow A\)
1. \(\frac{(2\hat i -\hat j)}{2}\)
2. \(\frac{5}{2}(\hat i - \hat j)\)
3. \(\frac{5}{2}(\hat i + \hat j)\)
4. \(\frac{(3\hat i -2\hat j)}{2}\)
If a vector is inclined at angles \(\alpha ,\beta ,~\text{and}~\gamma\), with \(x\), \(y\), and \(z\)-axis respectively, then the value of \(\sin^{2}\alpha+\sin^{2}\beta+ \sin^{2}\gamma\)
is equal to:
1. \(0\)
2. \(1\)
3. \(2\)
4. \(\frac{1}{2}\)
A force of \(20\) N acts on a particle along a direction, making an angle of \(60^\circ\) with the vertical. The component of the force along the vertical direction will be:
1. | \(2\) N | 2. | \(5\) N |
3. | \(10\) N | 4. | \(20\) N |
If \(\overrightarrow {A}\) \(\overrightarrow{B}\) are two vectors inclined to each other at an angle \(\theta,\) then the component of \(\overrightarrow {A}\) perpendicular to \(\overrightarrow {B}\) and lying in the plane containing \(\overrightarrow {A}\) and \(\overrightarrow {B}\) will be:
1. \(\frac{\overrightarrow {A} \overrightarrow{.B}}{B^{2}} \overrightarrow{B}\)
2. \(\overrightarrow{A} - \frac{\overrightarrow{A} \overrightarrow{.B}}{B^{2}} \overrightarrow{B}\)
3. \(\overrightarrow{A} -\overrightarrow{B}\)
4. \(\overrightarrow{A} + \overrightarrow{B}\)
If \(\left|\overrightarrow A\right|\ne \left|\overrightarrow B\right|\) and \(\left|\overrightarrow A \times \overrightarrow B\right|= \left|\overrightarrow A\cdot \overrightarrow B\right|\), then:
1. | \(\overrightarrow A \perp \overrightarrow B\) |
2. | \(\overrightarrow A ~|| ~\overrightarrow B\) |
3. | \(\overrightarrow A\) is antiparallel to \(\overrightarrow B\) |
4. | \(\overrightarrow A\) is inclined to \(\overrightarrow B\) at an angle of \(45^{\circ}\) |
Two forces of the same magnitude are acting on a body in the East and North directions, respectively. If the body remains in equilibrium, then the third force should be applied in the direction of:
1. North-East
2. North-West
3. South-West
4. South-East
Given are two vectors, \(\overrightarrow{A} = \left(\right. 2 \hat{i} - 5 \hat{j} + 2 \hat{k} \left.\right)\) and \(\overrightarrow{B} = \left(4 \hat{i} - 10 \hat{j} + c \hat{k} \right).\) What should be the value of \(c\) so that vector \(\overrightarrow A \) and \(\overrightarrow B\) would becomes parallel to each other?
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
If \(\overrightarrow{A} \times \overrightarrow{B} = \overrightarrow{C} + \overrightarrow{D}\), then which of the following statement is correct?
1. | \(\overrightarrow B\) must be perpendicular to \(\overrightarrow C\) |
2. | \(\overrightarrow A\) must be perpendicular to \(\overrightarrow C\) |
3. | Component of \(\overrightarrow C\) along \(\overrightarrow A\) = Component of \(\overrightarrow D\) along \(\overrightarrow A\) |
4. | Component of \(\overrightarrow C\) along \(\overrightarrow A\) = - (Component of \(\overrightarrow D\) along \(\overrightarrow A\)) |
What is the maximum value of \(5\sin\theta-12\cos\theta\)?
1. \(12\)
2. \(17\)
3. \(7\)
4. \(13\)
A block of weight \(W\) is supported by two strings inclined at \(60^{\circ}\) and \(30^{\circ}\) to the vertical. The tensions in the strings are \(T_1\) and \(T_2\) as shown. If these tensions are to be determined in terms of \(W\) using the triangle law of forces, which of these triangles should you draw? (block is in equilibrium):
1. | 2. | ||
3. | 4. |