If \(\overrightarrow{\mathbf{A}}{=}{2}\hat{i}+\hat{j}\;{\&}\;\overrightarrow{\mathbf{B}}{=}\hat{i}{-}\hat{j}\) , then the components of along with & perpendicular to respectively will be:
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If \(\vec{a}\) is a vector and \(x\) is a non-zero scalar, then which of the following is correct?
1. \(x\vec{a}\) is a vector in the direction of \(\vec{a}\)
2. \(x\vec{a}\) is a vector collinear to \(\vec{a}\)
3. \(x\vec{a}\) and \(\vec{a}\) have independent directions
4. \(x\vec{a}\) is a vector perpendicular to \(\vec{a}\)
The vector , which is collinear with the vector =(2, 1, -1) and satisfies the condition .=3 is-
1. (1, 1/2, -1/2)
2. (2/3, 1/3, -1/3)
3. (1/2, 1/4, -1/4)
4. (1, 1, 0)
If a, b and c are three non-zero vectors such that , then the value of will be:
1. | Less than zero | 2. | equal to zero |
3. | greater than zero | 4. | 3 |
What is the torque of a force newton acting at a point metre about the origin? (Given: )
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The momentum of a body moving in a straight line is . Force acting on the body at t=2 sec will be: (\(Given: F=\frac{dp}{dt}\))
1. 6 N
2. 8 N
3. 4 N
4. 2 N
Temperature of a body varies with time as , where is the temperature in Kelvin at , then the rate of change of temperature at is:
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and are two vectors and θ is the angle between them. If , then the value of θ will be:
1. | 60o | 2. | 45o |
3. | 30o | 4. | 90o |
A particle is moving along the x-axis. The velocity v of this particle varies with its position x as . Find the velocity of the particle as a function of time t given that at t=0, x=1 and v=.
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4. None of these