A river is flowing from east to west at a speed of $5\ m/min$ . A man on south bank of river, capable of swimming $10\ m/min$ in still water, wants to swim across the river in shortest time. He should swim
Due north
Due north-east
Due north-east with double the speed of river
None of these
The angle between the two vectors $\vec A = 3\hat i + 4\hat j + 5\hat k$ and $\vec B = 3\hat i + 4\hat j + 5\hat k$ is ....... $^o$
$A =2 \hat{ i }+\hat{ j }, B =3 \hat{ j }-\hat{ k }$ and $C =6 \hat{ i }-2 \hat{ k }$ Value of $A -2 B +3 C$ would be
A vector $\overrightarrow a $ is turned without a change in its length through a small angle $d\theta .$The value of $|\Delta \overrightarrow a |$ and $\Delta a$ are respectively