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Find the equation of the plane passin...

Find the equation of the plane passing through `(3,4,-1),` which is parallel to the plane ` vec rdot(2 hat i-3 hat j+5 hat k)+7=0.`

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The equation of any plane which is parallel to `vecr*(2hati-3hatj+5hatk)+7=0` is
`" "vecr*(2hati-3hatj+5hatk)+lamda=0" "` (i)
or `" "2x-3y+5z+lamda=0`
Further (i) will pass through (3, 4, -1) if `(2)(3)+(-3)(4)+5(-1)+lamda=0 or -11+lamda=0 or lamda=0 or lamda=11`
Thus, equation of the required plane is `vecr*(2hati-3hatj+5hatk)+11=0`.
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