Two vectors $\vec A$ and $\vec B$ have equal magnitudes. The magnitude of $(\vec A + \vec B)$ is $‘n’$ times the magnitude of $(\vec A - \vec B)$. The angle between $ \vec A$ and $\vec B$ is
${\cos ^{ - 1}}\left[ {\frac{{{n^2} - 1}}{{{n^2} + 1}}} \right]$
${\cos ^{ - 1}}\left[ {\frac{{n - 1}}{{n + 1}}} \right]$
${\sin ^{ - 1}}\left[ {\frac{{{n^2} - 1}}{{{n^2} + 1}}} \right]$
${\sin ^{ - 1}}\left[ {\frac{{n - 1}}{{n + 1}}} \right]$
$\overrightarrow{ A }=4 \hat{ i }+3 \hat{ j }$ and $\overrightarrow{ B }=4 \hat{ i }+2 \hat{ j }$. Find a vector parallel to $\overrightarrow{ A }$ but has magnitude five times that of $\vec{B}$.
The vectors $\vec{A}$ and $\vec{B}$ are such that
$|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$
The angle between the two vectors is
If two vectors $2\hat i + 3\hat j - \hat k$ and $ - 4\hat i - 6\hat j + \lambda \hat k$ are parallel to each other then value of $\lambda$ be
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 ?