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Find the vector equation of the line passing through the point having position vector ijk-2i^+j^+k^ and parallel to vector ijk4i^-j^+2k^. - Mathematics and Statistics

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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"`.

Sum
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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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Vector and Cartesian Equations of a Line
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Chapter 6: Line and Plane - Exercise 6.1 [Page 200]

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