Using dot product, find a perpendicular vector to
u=(9,2] *components
How can I solve this question?
Hi, theowne. Two vectors are considered perpendicular, or orthogonal, if their dot product is zero. So, let the desired vector be $\displaystyle v = \left(v_1,\;v_2\right)$. Then, we have:
$\displaystyle u\cdot v = 0\Rightarrow \left(9,\;2\right)\cdot\left(v_1,\;v_2\right) = 0\Rightarrow 9v_1 + 2v_2 = 0$.
Solve for one component, and just pick a value for the independent one.
You won't be able to find a unique solution. It should be obvious that there are infinitely many vectors perpendicular to a given vector, so if you only want one you will have to pick arbitrarily.
So, solve for one of the variables in terms of the other, and then pick an arbitrary value for the second component to find the corresponding value for the first.
Or, if you want the general solution (i.e., all possible solutions), introduce a parameter (for example, let $\displaystyle v_2 = t$ and then solve for $\displaystyle v_1$ in terms of $\displaystyle t$).
Does that make sense?