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Question
Find the distance of the point (−1, −5, −10) from the point of intersection of the line `vecr = 2hati -hatj + 2hatk + lambda(3hati + 4hatj + 2hatk)` and the plane `vecr.(hati -hatj + hatk) = 5`.
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Solution
The equation of the given line is
`vecr = 2hati -hatj + 2hatk + lambda(3hati + 4hatj + 2hatk)`
The equation of the given plane is
`vecr.(hati -hatj + hatk) = 5`
Substituting the value of `vecr` from equation (1) in equation (2), we obtain
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