Hello guys I have two simple tasks in linear algebra I have to figure out how to solve.
Vector $a = (k,1,k+1)$ Vector $b = (-1,2,1-k)$
Question 1: For which value of $k$ is the length ob vector $a + b$ the same length as vector $a - b$? Is $k=1$ correct?
Question 2: For which values of $k$ are the vectors $a + b$ and $a - b$ orthogonal?
Thanks a lot guys!
Edit added: for the first question I calculated vector ${\underline{a}+\underline{b}}$ and ${\underline{a}-\underline{b}}$ and then calculated the norms which I equated. for the second question I calculated vector ${\underline{a}+\underline{b}}$ and ${\underline{a}-\underline{b}}$ again and now calculated the scalar product which I equated to zero. Problem is I don't even know if this is the right way of doing it.