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Question
Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector `3hati+2hatj-2hatk`.
Solution
`3hati + 2hatj - 2hatk`
The given line passes through point A(1, 2, 3) and is parallel to the vector `vecb = 3hati + 2hatj - 2hatk`.
Position vector of point A `vec(r_1) = hati + 2hatj - 3hatk`
∴ Vector equation of a given line `vecr = vec(r_1) + λ vecb`
Or `vecr = (hati + 2hatj + 3hatk) + λ(3hati + 2hatj - 2hatk)` where λ is a scalar.
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