Question 762394
if 
{{{A = 3i - 2j +k}}} , 
{{{B= i -3j + 5k}}} , 
{{{C= 2i + j - 4k}}} form a right angled triangle, then they satisfy Pythagorean theorem

{{{C^2=A^2+B^2}}}

if 
{{{A = 3i - 2j +k}}} , 
{{{B= i -3j + 5k}}} , 
{{{C= 2i + j - 4k}}}

{{{A+B = C}}}, 
{{{A}}}, {{{B}}}&{{{C}}} represents sides of the triangle

Then 
{{{A = sqrt(9 +4 +1)=sqrt(14)}}} units

{{{B= sqrt(1 +9 + 25)=sqrt(35)}}}

{{{C= sqrt(4 + 1 +16)=sqrt(21)}}}

since  {{{C^2=A^2+B^2}}} = >  {{{(sqrt(35))^2=(sqrt(14))^2+(sqrt(21))^2}}} 
 = >  {{{35=14+21}}} 
 = >  {{{35=35}}} ...it's true, so  the triangle is right angled triangle