List of top Physics Questions on Vector Calculus

Find \( \nabla\phi \) if \( \phi = \log r \), where \( r = |\vec{r}| \):
The condition that the vector \(\vec{A}\) should be a gradient of a scalar function is:
The value of \(a\), \(b\) and \(c\) such that \(\vec{F} = (3x - 4y + az)\hat{i} + (cx - 5y - 2z)\hat{j} + (x - by + 7z)\hat{k}\) is irrotational, are respectively:
The torque due to the force \( \left( 2\hat{i} + \hat{j} + 2\hat{k} \right) \) about the origin, acting on a particle whose position vector is \( \hat{i} + \hat{j} + \hat{k} \), would be:
The torque due to the force \( \left( 2\hat{i} + \hat{j} + 2\hat{k} \right) \) about the origin, acting on a particle whose position vector is \( \hat{i} + \hat{j} + \hat{k} \), would be: