Basic mathematics3 questions.

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#	Question
1	Show that $underline{a}.underline{a}=0$ If $underline{a}=left langle 0,1,2 ight angle$ and $underline{b}=left langle 3,1,0 ight angle$ find $underline{a} imes underline{b}$ $underline{b} imes underline{a}$ If $underline{a}=left langle -4,0,3 ight angle$ , $underline{b}=left langle 2,-1,0 ight angle$ and $underline{c}=left langle 0,2,1 ight angle$ show that $underline{a} imes(underline{b} imesunderline{c}) eq (underline{a} imesunderline{b}) imesunderline{c}$ . Mathematical Calculation
2	Find the unit vector perpendicular to both $underline{a}=underline{i}+3underline{j}+4underline{k}$ and $underline{b}=2underline{i}+2underline{j}+underline{k}$ If $underline{a}=left langle 0,1,2 ight angle$ and $underline{b}=left langle 1,0,1 ight angle$ show that vector $underline{a} imes underline{b}$ is perpendicular to both $underline{a}$ and $underline{b}$ . Prove that $(underline{a}-underline{b}) imes (underline{a}+underline{b})=2(underline{a} imesunderline{b})$ Mathematical Calculation
3	If $underline{a}$ , $underline{b}$ and $underline{c}$ are vectors in $V_{3}$ , show that $underline{a}.(underline{b}+underline{c})=underline{a}.underline{b} + underline{a}.underline{c}$ Given $\|underline{r} imesunderline{s}\|=sqrt{35}$ and if $underline{r}=2underline{i}+underline{j}-underline{k}$ and $underline{s}=3underline{i}+lambda underline{j}+underline{k}$ find the exact value(s) of $lambda$ . Mathematical Calculation