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Question
Find the vector equation of the line passing through the point having position vector `3hat"i" + 4hat"j" - 7hat"k"` and parallel to `6hat"i" - hat"j" + hat"k"`.
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Solution
The vector equation of the line passing through A(`bar(a))` and parallel to the vector `bar"b"` is `bar"r" = bar"a" + lambdabar"b"`, where `lambda` is a scalar.
∴ the vector equation of the line passing through the point having position vector
`3hat"i" + 4hat"j" - 7hat"k"` and parallel to the vector `6hat"i" - hat"j" + hat"k"` is
`bar"r" = (3hat"i" + 4hat"j" -7hat"k") + lambda(6hat"i" - hat"j" + hat"k")`.
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