Prove that a right angled triangle can be formed using the vectors `vecA=hati-3hatj+5hatk, vecB=2hati+hatj-4hatk and vecC=3hati-2hatj+hatk`.

Explanation

`vecA+vecB=(hati-3hatj+5hatk)+(2hati+hatj-4hatk)=3hati-2hatj+hatk=vecC`
`i.e., vecA+vecB=vecC`
So, `vecA,vecB and vecC` can form a triangle .
Again , `vecB*vecC=(2hati+hatj-4hatk)*(3hati-2hatj-hatk)=6-2-4=0`
`therefore` In the triangle formed by `vecA,vecB and vecC` , the angle between `vecB and vecC is 90^@`. Thus , it is a right -angled triangle.
[The dot product `vecB*vecC` has been calculated , because `vecA` forms the largest side of the triangle .
An angle of `90^@` is always opposite to the largest side .
In this example, `A=sqrt(35),B=sqrt(21) and C=sqrt(14) i.e., Agt B,C]`