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Question
Find the vector equation of the line passing through the point having position vector `-2hat"i" + hat"j" + hat"k" "and parallel to vector" 4hat"i" - hat"j" + 2hat"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" + λbar"b"`, where λ is a scalar.
∴ the vector equation of the line passing through the point having position vector `-2hat"i" + hat"j" + hat"k" "and parallel to the vector" 4hat"i" - hat"j" + 2hat"k"` is `bar"r" = (-2hat"i" + hat"j" + hat"k") + lambda(4hat"i" - hat"j" + 2hat"k").`
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