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Question
Find the direction cosines of the lines `bar"r" = (-2hat"i" + 5/2hat"j" - hat"k") + lambda(2hat"i" + 3hat"j")`.
Solution
The line `bar"r" = (-2hat"i" + 5/2hat"j" - hat"k") + lambda(2hat"i" + 3hat"j")` is parallel to `bar"b" = 2hat"i" + 3hat"j"`.
∴ direction ratios of the line are 2, 3, 0
∴ direction cosines of the line are
`(2)/sqrt(2^2 + 3^2 + 0), (3)/sqrt(2^2 + 3^2 + 0), 0`
i.e. `(2)/sqrt(13), (3)/sqrt(13), 0`.
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