Question

Find the angle between the lines `vec"r" = 3hat"i" - 2hat"j" + 6hat"k" + lambda(2hat"i" + hat"j" + 2hat"k")` and `vec"r" = (2hat"j" - 5hat"k") + mu(6hat"i" + 3hat"j" + 2hat"k")`

Answer 1

Here, `vec"b"_1 = 2hat"i" + hat"j" + 2hat"k"` and `vec"b"_2 = 6hat"i" + 3hat"j" + 2hat"k"`

∴ `cos theta = (vec"b"_1 * vec"b"_2)/(|vec"b"_1||vec"b"_2|)`

= `((2hat"i" + hat"j" + 2hat"k")*(6hat"i" + 3hat"j" + 2hat"k"))/(sqrt((2)^2 + (1)^2 + (2)^2) * sqrt((6)^2 + (3)^2 + (2)^2)`

= `(12 + 3 + 4)/(sqrt(4 + 1 + 4) * sqrt(36 + 9 + 4)`

= `19/(sqrt(19) * sqrt(49)`

= `19/(3*7)`

= `19/21`

∴ `theta = cos^-1 (19/21)`

Hence, the required angle is `cos^-1 (19/21)`.