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The primitive translation vectors of the body centred cubic lattice are $$\overrightarrow {\bf{a}} = \frac{a}{2}\left( {{\bf{\hat x}} + {\bf{\hat y}} - {\bf{\hat z}}} \right),\,\overrightarrow {\bf{b}} = \frac{a}{2}\left( { - {\bf{\hat x}} + {\bf{\hat y}} + {\bf{\hat z}}} \right)$$        and $$\overrightarrow {\bf{c}} = \frac{a}{2}\left( {{\bf{\hat x}} - {\bf{\hat y}} + {\bf{\hat z}}} \right)$$    . The primitive translation vectors $$\overrightarrow {\bf{A}} ,\,\overrightarrow {\bf{B}} $$  and $$\overrightarrow {\bf{C}} $$ of the reciprocal lattice are
If the resultant of \(\vec{A}=6\hat{A}\) and \(\vec{B}=8\hat{B}\) is \(\vec{R}=10\hat{R}\) where \(\hat{A},\hat{B}\) and \(\hat{R}\) are the unit vectors along \(\vec{A},\vec{B}\) and \(\vec{R}\), then the value of \(\vec{A}\cdot \vec{B}\) will be
Rima is traveling in her car at the speed of 60 km/hr. She drops her hat and didn’t recognize it for 10 minutes, during this time the hat travels due to air drag. As soon as she recognizes this she turns her car around and drive 50% faster to get her favourite hat, so that she could get her hat after 15 minutes after the fall. Find the average speed of the hat with which it travelled till it was caught.
$${\bf{\hat A}}$$ and $${\bf{\hat B}}$$ represent two physical characteristics of a quantum system. If $${\bf{\hat A}}$$ is Hermitian, then for the product $${\bf{\hat A\hat B}}$$  to be Hermitian, it is sufficient that
Akshara was travelling in her boat when the wind blew her hat and hat started floating back stream. The boat continued to travel upstream for twelve minutes after which Akshara realized that her hat had fallen off and turned back downstream. She caught up with that as soon as it reached the starting point. Find the speed of river if Akshara’s hat flew off exactly 3 km from where she started?
$${{\bf{\hat A}}}$$ and $${{\bf{\hat B}}}$$ are two quantum mechanical operators. If $$\left[ {{\bf{\hat A}},\,{\bf{\hat B}}} \right
Which of the following is the correct vector multiplication in terms of \(\hat{i}\), \(\hat{j}\) and \(\hat{k}\)?
A rod of length L with uniform charge density $$\lambda $$ per unit length is in the XY-plane and rotating about Z-axis passing through one of its edge with an angularvelocity $$\overrightarrow \omega $$ as shown in the figure below. $$\left( {{\bf{\hat r}},\,\hat \phi ,\,{\bf{\hat z}}} \right)$$   refer to the unit vectors at Q, $$\overrightarrow {\bf{A}} $$ is the vector potential at a distance d from the origin O along Z-axis for d ≪ L and $$\overrightarrow {\bf{J}} $$ is the current density due to the motion of the rod. Which one of the following statements is correct?
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Suresh Kumar was rowing upstream on the Brahmaputra River. When he had covered one kilometer from his starting point, his hat fell into the river and started floating downstream. Suresh continued to row upstream for five more minutes before he realized that his hat had fallen off. He then, turned back and caught up with the hat just as it reached the starting point. Then, what is the speed of the flow of the river?
A son and father goes for boating in river upstream . After rowing for 1 mile son notices the hat of his father falling in the river. After 5 min he tells his father that his hat has fallen. So they turn round and are able to pick the hat at the point from where they began boating after 5min. Find the speed of river in miles/hours ?