Question

Given that a, b is a pair of non-collinear vectors such that $(3h+k)a+(1-2h)b=ha+2kb$. find $|2(h\ast k)|$ ?

Answer 1

From given equation we get $(2h+k)a+(1-2h-2k)b=0$

Since $a,b$ are non zeros.

We get $2h+k=0$ and $2h+2k=1$

By subtracting these two, we get $k=1$, from that we get $h=-1/2$

So $|2(h\ast k)|=1$