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The vectors u=mxvector i+2xvector j, vector v=3xvector i-vector j are perpendicular ....

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ruals | Salutatorian

Posted July 23, 2013 at 4:47 PM via web

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The vectors u=mxvector i+2xvector j, vector v=3xvector i-vector j are perpendicular . what is m?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 23, 2013 at 5:08 PM (Answer #1)

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The problem provides the information that the vectors  are orthogonal, hence, evaluating its dot product yields 0.

`bar u*bar v = 0`

You need to perform the multiplication of the vectors `bar u` and `bar v` , such that:

`(m*bar i + 2*bar j)(3*bar i - bar j) = 0`

`m*bar^2 i - m*bar i*bar j + 6*bar i*bar j - 2bar^2 j = 0`

Since `bar i*bar j = 0` and `bar^2 i = bar^2 j = 1` yields:

`m - 2 = 0 => m = 2`

Hence, evaluating m, using the information that `bar u` is perpendicular to `bar v` , yields `m = 2.`

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