# Direction cosines

1. Sep 12, 2015

### Rahul Manavalan

• Member warned about posting with no effort
1. The problem statement, all variables and given/known data
To find the direction cosine of a equation say (4x+5y+7z=13)

2. Relevant equations

Im not really sure what to do

3. The attempt at a solution
(I know this is really basic but i would be glad if someone helps me with this

2. Sep 12, 2015

### SammyS

Staff Emeritus
Is that the complete question?

What have you tried? Where are you stuck ?

What is that the equation of?

How can such an object have direction cosines?

3. Sep 12, 2015

### SteamKing

Staff Emeritus
Looks like the equation for a plane. How do you usually find a normal to a plane?

4. Sep 14, 2015

### HallsofIvy

The problem appears to be that the OP really does NOT understand the basics of three dimensional lines. Rahul, as SteamKing said, the equation you give defines a plane in three dimensions, not a line. The "direction cosines" of a line in three dimensions are the cosines of the angles the line makes with lines parallel to the three coordinate axes. In addition, They are the dot products of a unit vector in the direction of the line with unit vectors in the directions of the three coordinate axes. In particular, if a line is given in parametric form, x= at+ b, y= ct+ d, z= et+ f, then the vector ai+ bj+ ck is in the direction of the line. Dividing by $\sqrt{a^2+ b^2+ c^2}$ is gives a unit vector in that direction. In other words, the three direction cosines are $\frac{a}{\sqrt{a^2+ b^2+ c^2}}$, $\frac{b}{\sqrt{a^2+ b^2+ c^2}}$, and $\frac{c}{\sqrt{a^2+ b^2+ c^2}}$.