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Find the Vector Equation of the Lines Which Passes Through the Point with Position Vector `4hati - Hatj +2hatk` And Is in the Direction of `-2hati + Hatj + Hatk` - Mathematics and Statistics

Find the vector equation of the lines which passes through the point with position vector `4hati - hatj +2hatk` and is in the direction of `-2hati + hatj + hatk`

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Solution

Let `bara = 4hati - hatj + 2hatk`

`barb = -hat2i + hatj + hatk`

Equation of the line passing through point `A(bara)` and having direction `barb` is

`barr = bara + lambdabarb`

`barr = (4hati - hatj + 2hatk) + lambda(-2hati + hatj + hatk)`

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