What do you mean by weird? In any case, your method, at least to me, seems to be a bit of overkill. Why not just solve the system of equations the usual way?ezsmith said:Homework Statement
Find cartesian equations of the line of intersection of the planes x+3y-6z =2 and 2x+7y-3z=7
The Attempt at a Solution
What I did first was I cross product the 2 equation and then I got 33i-9j+k
Then I took both of the equation and let y = 0. After that my answer seems to be weird.. Did I did anything wrong? The answer of the book was given ∴x+7/33 = y-3/-9 = z
vela said:What do you mean by weird? In any case, your method, at least to me, seems to be a bit of overkill. Why not just solve the system of equations the usual way?
A cartesian equation is an algebraic equation that relates variables x, y, and z in a three-dimensional coordinate system. It consists of terms with powers of x, y, and z and coefficients, and it can be used to represent geometric shapes such as lines, planes, and curves.
To find the cartesian equation of a line of intersection, you will need to have the equations of two intersecting planes. You can then set the equations equal to each other and solve for two of the variables, leaving the third variable as a free parameter. This will give you the cartesian equation for the line of intersection.
The cartesian equation of a line of intersection can be used to determine the points where two planes intersect in three-dimensional space. This information can be useful in various applications, such as determining the angle between two planes or finding the shortest distance between two objects in space.
Yes, there are alternative methods for finding the cartesian equation of a line of intersection. One method is to use vector equations, where the line of intersection can be represented by the cross product of the normal vectors of the two planes. Another method is to use parametric equations, where the line of intersection can be expressed in terms of a parameter.
No, the cartesian equation of a line of intersection can only be used for linear equations. Non-linear equations will result in curved surfaces, making it impossible to find a single equation that represents the line of intersection. In these cases, other methods such as using parametric equations or vector equations may be necessary.