Homework Help: Finding the direction vector with only direction angles

1. Nov 2, 2005

nicole

Hey everybody! Thanks for any help!

If I am told a line has direction angles of 60, 45 and 60 and passes through the point (-2, 1, 3). How would I go about figuring out the symmetric equations of the line..

Relatively simple question but I am a tad confused. HELP!
THANKS AGAIN!

2. Nov 3, 2005

HallsofIvy

If $$\theta$$, $$\phi$$, and $$\psi$$ are the "direction angles", then $$cos(\theta)$$, $$cos(\phi)$$, and $$cos(\psi)$$, the "direction cosines", form a unit vector in that direction.
cos(60)= 1/2, cos(45)= $$\frac{\sqrt{2}}{2}$$ so a unit vector in the direction with direction angles 60, 45, 60 (degrees- it would be good idea to say that explicitely!) is $$\frac{1}{2}i+ \frac{\sqrt{2}}{2}j+ \frac{1}{2}k$$ and parametric equations for a line in that direction, passing through (-2, 1, 3) would be $$x= \frac{1}{2}t- 2$$, $$y= \frac{\sqrt{2}}{2}t+ 2$$, $$z= \frac{1}{2}t+ 3$$.