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Find a vector magnitude 5 units, and ...

Find a vector magnitude 5 units, and parallel to the resultant of the vectors ` vec a=2 hat i+3 hat j- hat k` and ` vec b= hat i-2 hat j+ hat kdot`

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To solve the problem of finding a vector with a magnitude of 5 units that is parallel to the resultant of the vectors \( \vec{a} = 2\hat{i} + 3\hat{j} - \hat{k} \) and \( \vec{b} = \hat{i} - 2\hat{j} + \hat{k} \), we will follow these steps: ### Step 1: Find the resultant vector \( \vec{c} \) The resultant vector \( \vec{c} \) is obtained by adding vectors \( \vec{a} \) and \( \vec{b} \). \[ \vec{c} = \vec{a} + \vec{b} = (2\hat{i} + 3\hat{j} - \hat{k}) + (\hat{i} - 2\hat{j} + \hat{k}) \] ...
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