If a particle moves from point $P (2,3,5)$ to point $Q (3,4,5)$. Its displacement vector be
$\hat i + \hat j + 10\hat k$
$\hat i + \hat j + 5\hat k$
$\hat i + \hat j$
$2\hat i + 4\hat j + 6\hat k$
The three vectors $\overrightarrow A = 3\hat i - 2\hat j + \hat k,\,\,\overrightarrow B = \hat i - 3\hat j + 5\hat k$ and $\overrightarrow C = 2\hat i + \hat j - 4\hat k$ form
A person moves $30\, m$ north and then $20\, m$ towards east and finally $30\sqrt 2 \,m$ in south-west direction. The displacement of the person from the origin will be
Two vectors $\overrightarrow{ A }$ and $\overrightarrow{ B }$ have equal magnitudes. If magnitude of $\overrightarrow{ A }+\overrightarrow{ B }$ is equal to two times the magnitude of $\overrightarrow{ A }-\overrightarrow{ B }$, then the angle between $\overrightarrow{ A }$ and $\overrightarrow{ B }$ will be .......................
Establish the following vector inequalities geometrically or otherwise:
$(a)$ $\quad| a + b | \leq| a |+| b |$
$(b)$ $\quad| a + b | \geq| a |-| b |$
$(c)$ $\quad| a - b | \leq| a |+| b |$
$(d)$ $\quad| a - b | \geq| a |-| b |$
When does the equality sign above apply?