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Question
Find the vector equation of the line `x/1 = (y - 1)/2 = (z - 2)/3`
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Solution
The given equation of a line passes through the point A(0, 1, 2) and the direction ratios of the line are 1, 2, 3.
Let `bar"a"` be the position vector of point A.
Let `bar"b"` be the vector parallel to this line.
∴ `bar"a" = hat"j" + 2hat"k"` and `bar"b" = hat"i" + 2hat"j" + 3hat"k"`
The vector equation of a line passing through a point with position vector `bar"a"` and parallel to `bar"b"` is `bar"r" = bar"a" + lambdabar"b"`.
The vector equation of the given line is `bar"r" = (hat"j" + 2hat"k") + lambda(hat"i" + 2hat"j" + 3hat"k")`
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