Question

if $|\stackrel{\rightarrow}{a}+\stackrel{\rightarrow}{b}|$ =60, $|\stackrel{\rightarrow}{a}-\stackrel{\rightarrow}{b}|$=40 and $\stackrel{\rightarrow}{a}\$=22,then find $\stackrel{\rightarrow}{b}\$.

If $|\stackrel{\rightarrow}{a}|$=2, $|\stackrel{\rightarrow}{b}|$=3 and $\stackrel{\rightarrow}{a}$.$\stackrel{\rightarrow}{b}$=3 then find the projection of $|\stackrel{\rightarrow}{b}|$ on $|\stackrel{\rightarrow}{a}|$.

If $\stackrel{\rightarrow}{a}\$and $\stackrel{\rightarrow}{b}\$ are two unit vectors such that $\stackrel{\rightarrow}{a}\$ +$\stackrel{\rightarrow}{b}\$ is also a unit vector, then find the angle between $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$

Find $|\stackrel{\rightarrow}{x}|\$, if for a unit vector $\stackrel{\rightarrow}{a}\$ and ($\stackrel{\rightarrow}{x}\$ + $\stackrel{\rightarrow}{a}\$ )($\stackrel{\rightarrow}{x}\$ -$\stackrel{\rightarrow}{a}\$ ) = 15.

If $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$ are unit vectors, then what is the angle between $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$, so that ${\sqrt{2}}$ $\stackrel{\rightarrow}{a}\$ -$\stackrel{\rightarrow}{b}\$ is a unit vector ?

Give an example of vectors $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$ such that $\vert{\vec{b}}\vert=$ $\vert{\vec{b}}\vert$ but $\stackrel{\rightarrow}{a}\neq \stackrel{\rightarrow}{b}\;.$  

Find $\stackrel{\rightarrow}{a}$.$\stackrel{\rightarrow}{b}$,If $\stackrel{\rightarrow}{a}$ = $-\stackrel{\wedge}{i}+\stackrel{\wedge}{j} -2\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{b}$ = $2\stackrel{\wedge}{i}+3\stackrel{\wedge}{j} -\stackrel{\wedge}{k}$.