Given : $\vec A\, = \,2\hat i\, + \,p\hat j\, + q\hat k$ and $\vec B\, = \,5\hat i\, + \,7\hat j\, + 3\hat k,$ if $\vec A\,||\,\vec B,$ then the values of $p$ and $q$ are, respectively
$\frac {14}{5}$ and $\frac {6}{5}$
$\frac {14}{3}$ and $\frac {6}{5}$
$\frac {6}{5}$ and $\frac {1}{3}$
$\frac {3}{4}$ and $\frac {1}{4}$
Two forces of magnitude $P$ & $Q$ acting at a point have resultant $R$. The resolved part of $R$ in the direction of $P$ is of magnitude $Q$. Angle between the forces is :
If the sum of two unit vectors is also a unit vector. then magnitude of their difference and angle between the two given unit vectors is ..............
A passenger arriving in a new town wishes to go from the station to a hotel located $10 \;km$ away on a straight road from the station. A dishonest cabman takes him along a circuitous path $23\; km$ long and reaches the hotel in $28 \;min$. What is
$(a)$ the average speed of the taxi,
$(b)$ the magnitude of average velocity ? Are the two equal ?
A cyclist starts from the centre $O$ of a circular park of radius $1\; km$, reaches the edge $P$ of the park, then cycles along the circumference, and returns to the centre along $QO$ as shown in Figure. If the round trip takes $10 \;min$, what is the
$(a)$ net displacement,
$(b)$ average velocity, and
$(c)$ average speed of the cyclist ?