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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`, ` ->alpha=3 hat i- hat j , ->beta=2 hat i+ hat j-3 hat k`, then express ` ->beta`in the from ` ->beta= ->beta_1+ ->beta_2`, where ` -

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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 follow these steps: ### Step 1: Identify the vectors Given: - \( \vec{\alpha} = 3\hat{i} - \hat{j} \) - \( \vec{\beta} = 2\hat{i} + \hat{j} - 3\hat{k} \) ### Step 2: Express \( \vec{\beta_1} \) in terms of \( \vec{\alpha} \) ...
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