Question

Given that a, b is a pair of non-collinear vectors such that $(1+2h-k)a+(2-h+2k)b=0$. Find $|h+k|$ ?

Answer 1

Since $\overline{a}$ and $\overline{b}$ are non col-linear, hence for the above expression to be zero, individual coefficients have to be 0.

Hence

$1+2h-k=0$

$2-h+2k=0$
Adding both the equations,

$h+k+3=0$
$h+k=-3$
$|h+k|=3$