I can't seem to show for question (a), I am not sure if it's because of my wrong calculation, or is it the question has the wrong values?
What I have done is I used the scalar product. I found that ${\vec{AB}} = (2,1,5); \vec{BC}=(2,1,-7)$. Then I tried taking the dot product between the two, and if it is a right-angled triangle, it means there should be two vectors that are perpendicular and that their dot product is $0$.
I have also tried doing that for ${\vec{AC}};\vec{BC}; \vec {BA}; \vec {CA}$ but none of them yielded $0$.
Please advise.
Sorry in advance for any wrong tags and title labelling.