Calculating Direction Cosines for Linear Equations - Homework Help

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The discussion centers on calculating direction cosines for the equation of a plane, specifically 4x + 5y + 7z = 13. Participants clarify that the equation represents a plane in three-dimensional space, not a line, which is crucial for understanding direction cosines. Direction cosines are defined as the cosines of the angles a line makes with the coordinate axes, derived from a unit vector in the line's direction. The solution involves identifying the normal vector to the plane and using it to find the direction cosines. Overall, the conversation emphasizes the need for a clear understanding of the relationship between planes and lines in three-dimensional geometry.
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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
 
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Rahul Manavalan said:

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?
 
Rahul Manavalan said:

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?
 
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}}.
 

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