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Find the vector equation of a line pa...

Find the vector equation of a line passing through `3 hat i-5 hat j+7 hat k` and perpendicular to theplane `3x-4y+5z=8.`

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The given plane `3x-4y+5z=8 or (3hati-4hatj+5hatk)*(xhati+yhatj+7hatk)=8.`
This shows that `vecd=3hati-4hatj+5hatk` is normal to the given plane.
Therefore, the required line is parallel to `3hati-4hatj+5hatk`.
Since the required line passes through `3hati-5hatj+7hatk`, its equation is given by
`" "vecr=3hati-5hatj+7hatk+lamda(3hati-4hatj+5hatk),` where `lamda` is a parameter.
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