If `vecA=3hati-2hatj+hatk, vecB =hati-3hatj+5hatk and vecB=hati-3hatj+5hatk, vecC=2hati+hatj-4hatk` from a right angled triangle then out of the following which one is satisfied ?

Options

A. `vecA =vecB+vecCand A^(2) =B^(2) +C^(2)`
B. `vecA=vecB+vecC and B^(2) =A^(2) +C^(2)`
C. `vecB =vecA+vecC and B^(2) =A^(2) +C^(2)`
D. `vecB =vecA+vecC and A^(2) =B^(2)+C^(2)`

Answer

B

Explanation

`A=sqrt(A _(x)^(2)+A_(y)^(2) +A_(z)^(2))=sqrt(9 +4=1 ) =sqrt14`
`B=sqrt(B_(x)^(2)+B_(y)^(2) +A_(z)^(2))=sqrt(1+ 9+ 25)=sqrt35`
`C=sqrt(C_(x)^(2)+C_(y)^(2) +C_(z)^(2))=sqrt(4+1+15)=sqrt21`
`B^(2) =A^(2) +C^(2)`