Answer
a) $i.j=j.k=k.i=0$
b) $i.i=j.j=k.k=1$
Work Step by Step
Angles between unit vectors $i$, $j$ and $k$ is 90 degrees.
a) $i.j= |i|*|j|*cos (\alpha)$, where $\alpha=90$
Since $cos(90)=0$
$i.j= |i|*|j|*cos (\alpha)= |i|*|j|*cos(90)=0$
$j.k= |j|*|k|*cos (\alpha)$, where $\alpha=90$
Since $cos(90)=0$
$j.k= |j|*|k|*cos (\alpha)= |j|*|k|*cos(90)=0$
$k.i= |k|*|i|*cos (\alpha)$, where $\alpha=90$
Since $cos(90)=0$
$k.i= |k|*|i|*cos (\alpha)= |k|*|i|*cos(90)=0$
b) We know that: $|i|=|j|=|k|=1$
$i.i= |i|*|i|*cos (\alpha)$, where $\alpha=0$
Since $cos(0)=1$
$i.i= |i|*|i|*cos (\alpha)= |i|*|i|*cos(0)=1*1*1=1$
$j.j= |j|*|j|*cos (\alpha)$, where $\alpha=0$
Since $cos(0)=1$
$j.j= |j|*|j|*cos (\alpha)= |j|*|j|*cos(0)=1*1*1=1$
$k.k= |k|*|k|*cos (\alpha)$, where $\alpha=0$
Since $cos(0)=1$
$k.k= |k|*|k|*cos (\alpha)= |k|*|k|*cos(0)=1*1*1=1$
