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Question
Find the vector equation of line passing through the point having position vector `5hat"i" + 4hat"j" + 3hat"k"` and having direction ratios –3, 4, 2.
Solution
Let A be the point whose position vector is a = `5hat"i" + 4hat"j" + 3hat"k"`.
Let `bar"b"` be the vector parallel to the line having direction ratio = –3, 4, 2
Then, `bar"b" = -3hat"i" + 4hat"j" + 2hat"k"`
The vector equation of the line passing through `"A"(bara)` and parallel to `bar"b" "is" bar"r" = bar"a" + lambdabar"b"`, where λ is a scalar.
∴ The required vector equation of the line is `bar"r" = 5hat"i" + 4hat"j" + 3hat"k" + lambda(-3hat"i" + 4hat"j" + 2hat"k").`
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