Calculating Direction Cosines for Linear Equations - Homework Help

[Rahul Manavalan]

Homework Statement

To find the direction cosine of a equation say (4x+5y+7z=13)

Homework Equations

Im not really sure what to do

The Attempt at a Solution

(I know this is really basic but i would be glad if someone helps me with this

 

[SammyS]

Homework Statement

To find the direction cosine of a equation say (4x+5y+7z=13)

Homework Equations

Im not really sure what to do

The Attempt at a Solution

(I know this is really basic but i would be glad if someone helps me with this

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?

 

[SteamKing]

Homework Statement

To find the direction cosine of a equation say (4x+5y+7z=13)

Homework Equations

Im not really sure what to do

The Attempt at a Solution

(I know this is really basic but i would be glad if someone helps me with this

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

 

[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}}.