Show that the vectors `a =3hati - 2hatj+hatk, b=hati - 3hatj+5hatk` and `c=2hatj+hatj-4hatk` form a right angled triangle.

Explanation

Given , `a=3hati-2hatj+5hatkand b=hati-3hatj+5hatk`
`c=2hati+hatj-4hatk`

We have `B+c=(hati-3hatj+5hatk)+(2hati_hatj-4hatk)`
`=3hati-2hatj+hatk=a`
hence ,abandc are coplana.
Also, We observe that no two of these vectors are vectors are parallel, therefore, thegiven vectors form a triangle .Further,
`a.c=(3hati-2hatj+hatk).(2hati+hatj- 4hatk )=O`
Dot product of two non-zero vectors is zero. hence ,they are perpendicular so they from a right angled triangle.
`therefore"magnitude of a,"|a|=sqrt(9+4+1)=sqrt(14),`
`"magnitude of b",|b|=sqrt(1+9+25)=sqrt(35)`
`"and magnitude of" c,|c|=sqrt(4+1+16)=sqrt(21)`