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Question
Find the vector equation of the line which is parallel to the vector `3hati - 2hatj + 6hatk` and which passes through the point (1 ,–2, 3).
Solution
Let `vecb = 3hati - 2hatj + 6hatk` and `veca = hati - 2hatj + 3hatk`
So, vector equation of the line
Which is parallel to the vector `vecb = 3hati - 2hatj + 6hatk`
And passes through the point `veca = hati - 2hatj + 3hatk` is `vecr = veca + lambdavecb`
∴ `vecr = (hati - 2hatj + 3hatk) + lambda(3hati - 2hatj + 6hatk)`
⇒ `(xhati + yhatj + zhatk) - (hati - 2hatj + 3hatk) - lambda(3hati - 2hatj + 6hatk)`
⇒ `(x - 1)hati + (y + 2)hatj + (z - 3)hatk = lambda(3hati - 2hatj + 6hatk)`
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