Find the values of x such that the given vectors are orthogonal. (Enter your answers from smallest to largest.)

xi + 3xj

xi - 5j

x = _______ (smaller value)

x = _______ (larger value)

The answer is 0 and 15, but how do I get that?

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- Sep 12th 2009, 07:24 PMxpackCan someone explain this to me?
Find the values of x such that the given vectors are orthogonal. (Enter your answers from smallest to largest.)

xi + 3xj

xi - 5j

x = _______ (smaller value)

x = _______ (larger value)

The answer is 0 and 15, but how do I get that? - Sep 12th 2009, 09:17 PMchisigma
Let's consider the two vectors as two complex numerrs...

... where is the 'imaginary unit'. The condition of orthogonality is...

... that leads at the algebraic equation...

... whose solution are and ...

Kind regards

- Sep 12th 2009, 09:30 PMwoof
They are orthogonal if, when you dot them, you get zero. So that gives you an equation to solve for x:

Now solve that by factoring. - Sep 12th 2009, 09:36 PMxpack
Thanks guys!