dot product of vector

**theowne** · May 19th 2008, 03:38 PM

Using dot product, find a perpendicular vector to

u=(9,2] *components

How can I solve this question?

**Reckoner** · May 19th 2008, 04:39 PM

Originally Posted by theowne

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 $v = \left(v_1,\;v_2\right)$ . Then, we have:

$u\cdot v = 0\Rightarrow \left(9,\;2\right)\cdot\left(v_1,\;v_2\right) = 0\Rightarrow 9v_1 + 2v_2 = 0$ .

Solve for one component, and just pick a value for the independent one.

**theowne** · May 19th 2008, 04:57 PM

How can I solve if there are two variables?

**Reckoner** · May 19th 2008, 05:04 PM

Originally Posted by theowne

How can I solve if there are two variables?

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 $v_2 = t$ and then solve for $v_1$ in terms of $t$ ).

Does that make sense?

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