Find unit vector perpendicular to $\vec A$ and $\vec B$ where $\vec A = \hat i - 2\hat j + \hat k$ and $\vec B = \hat i + 2\hat j$
$\frac{{2\hat i + \hat j + 4\hat k}}{{\sqrt {21} }}$
$\frac{{ - 2\hat i + \hat j + 4\hat k}}{{\sqrt {21} }}$
$\frac{{ - 2\hat i - \hat j + 4\hat k}}{{\sqrt {21} }}$
$\frac{{2\hat i + \hat j + 4\hat k}}{{\sqrt 5 }}$
The vectors $5i + 8j$ and $2i + 7j$ are added. The magnitude of the sum of these vector is
The five sides of a regular pentagon are represented by vectors $A _1, A _2, A _3, A _4$ and $A _5$, in cyclic order as shown below. Corresponding vertices are represented by $B _1, B _2, B _3, B _4$ and $B _5$, drawn from the centre of the pentagon.Then, $B _2+ B _3+ B _4+ B _5$ is equal to
The resultant of two forces $3P$ and $2P$ is $R$. If the first force is doubled then the resultant is also doubled. The angle between the two forces is ........... $^o$
Two forces $P$ and $Q$, of magnitude $2F$ and $3F$, respectively, are at an angle $\theta $ with each other. If the force $Q$ is doubled, then their resultant also gets doubled. Then, the angle $\theta $ is ....... $^o$
A bus is moving on a straight road towards north with a uniform speed of $50\; km / hour$ then it turns left through $90^{\circ} .$ If the speed remains unchanged after turning, the increase in the velocity of bus in the turning process is