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Find the equations of a line passing ...

Find the equations of a line passing through the point P(2,-1,3) and perpendicular to the lines
`vec(r ) =(hat(i) + hat(j) -hat(k)) +lambda (2hat(i) -2hat(j) +hat(k))`
and `vec( r) =(2hat(i) -hat(j) -3hat(k)) +mu (hat(i) +2hat(j) +2hat(k))`

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To find the equations of a line passing through the point \( P(2, -1, 3) \) and perpendicular to the given lines, we will follow these steps: ### Step 1: Identify the direction vectors of the given lines The first line is given by: \[ \vec{r} = \hat{i} + \hat{j} - \hat{k} + \lambda (2\hat{i} - 2\hat{j} + \hat{k}) \] ...
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