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Question
Find the vector equation of the lines passing through the point having position vector `(-hati - hatj + 2hatk)` and parallel to the line `vecr = (hati + 2hatj + 3hatk) + λ(3hati + 2hatj + hatk)`.
Solution
Let A be point having position vector `veca = -hati - hatj + 2hatk`.
The required Line is parallel to the line `vecr = (hati + 2hatj + 3hatk) + λ(3hati + 2hatj + hatk)`
∴ It is parallel to the vector `vecb = 3hati + 2hatj + hatk`
The vector equation of the line passing through A`(veca)` and parallel to `vecb` is r = `veca + λvecb` where λ is a scalar.
∴ The required vector equation of the line is `vecr = (-hati - hatj + 2hatk) + λ(3hati + 2hatj + hatk)`.
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