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If with reference to the right handed sy...

If with reference to the right handed system of mutually perpendicular unit vectors ` hat i , hat j`and ` hat k`, ` vecalpha=3 hat i- hat j , vecbeta=2 hat i+ hat j-3 hat k`, then express `vecbeta ` `` in the from `vecbeta=vecbeta_1+ vecbeta_2`, where `vecbeta_1` is parallel to `vecalpha` and `vecbeta_2` is perpendicular to `vecalpha`

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To express the vector \(\vec{\beta}\) in the form \(\vec{\beta} = \vec{\beta}_1 + \vec{\beta}_2\), where \(\vec{\beta}_1\) is parallel to \(\vec{\alpha}\) and \(\vec{\beta}_2\) is perpendicular to \(\vec{\alpha}\), we can follow these steps: ### Step 1: Define the vectors Given: \[ \vec{\alpha} = 3\hat{i} - \hat{j} \] \[ ...
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