Two forces having magnitude $A$ and $\frac{ A }{2}$ are perpendicular to each other. The magnitude of their resultant is
$\frac{\sqrt{5}\,A }{4}$
$\frac{5\,A }{2}$
$\frac{\sqrt{5}\,A ^2}{2}$
$\frac{\sqrt{5}\,A }{2}$
The resultant of $\vec A$ and $\vec B$ makes an angle $\alpha $ with $\vec A$ and $\beta $ with $\vec B$,
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?
Prove the associative law of vector addition.
What vector must be added to the two vectors $\hat i - 2\hat j + 2\hat k$ and $2\hat i + \hat j - \hat k,$ so that the resultant may be a unit vector along $X-$axis