You can
put this solution on YOUR website!I'm not sure how far you are in your course, but to find the angle between any two vectors, you would use this formula:
=\frac{\v{u}\cdot\v{v}}{\left|\v{u}\right|\left|\v{v}\right|})
where
is the magnitude (ie length) of vector
and
is the magnitude (ie length) of vector
So let's assume that
is true. That means we can replace
with 3
=\frac{3}{\left|\v{a}\right|\left|\v{b}\right|})
Now plug in the given magnitudes
and
=\frac{3}{1*2})
Now multiply the values in the denominator
=\frac{3}{2})
So this equation is implying that there is some value of
that will make
true. However, there is no such value. Remember, the range of cosine is
\le1)
. Since
equals 1.5 (which is greater than 1), it is outside the range of cosine. So if you try to take arccosine of both sides, you will not get a real answer for
So that means there are no two vectors that have magnitudes of 1 and 2 while having a dot product of 3.
