# If vector a=i(cap)+j(cap)+k(cap) and vector b= j(cap)-k(cap), find a vector c such that 'a' cross 'c' is vector b and 'a' dot 'c' is 3

let $c=x\stackrel{^}{i}+y\stackrel{^}{j}+z\stackrel{^}{k}$
given ;

$a·c=3\phantom{\rule{0ex}{0ex}}\left(\stackrel{^}{i}+\stackrel{^}{j}+\stackrel{^}{k}\right)·\left(x\stackrel{^}{i}+y\stackrel{^}{j}+z\stackrel{^}{k}\right)=3\phantom{\rule{0ex}{0ex}}x+y+z=3\phantom{\rule{0ex}{0ex}}1+z+z+z=3\phantom{\rule{0ex}{0ex}}3z=2\phantom{\rule{0ex}{0ex}}⇒z=\frac{2}{3}\phantom{\rule{0ex}{0ex}}x=1+\frac{2}{3}=\frac{5}{3}\phantom{\rule{0ex}{0ex}}y=\frac{2}{3}$
thus the required vector $c=\frac{5}{3}\stackrel{^}{i}+\frac{2}{3}\stackrel{^}{j}+\frac{2}{3}\stackrel{^}{k}$
hope this helps you

• -4
What are you looking for?