Question

Find the direction cosines of the lines `bar"r" = (-2hat"i" + 5/2hat"j" - hat"k") + lambda(2hat"i" + 3hat"j")`.

Answer 1

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`.