I am talking in generalPeterDonis said:What general equation are you starting from, and what do you think the canonical form is?
A reference would be helpful.
AhmedHesham said:We have the equations of the two planes
AhmedHesham said:How do we formulate the equation of the line in the canonical form
AhmedHesham said:The reference is my school book
AhmedHesham said:Let us discuss the solution
A straight line equation in space is an equation that represents a line in three-dimensional space. It is typically written in the form of Ax + By + Cz = D, where A, B, and C are the coefficients of the x, y, and z variables, and D is a constant.
An equation represents a straight line in space if it can be written in the form of Ax + By + Cz = D. This means that the equation must have three variables (x, y, and z) and no higher powers of these variables. Additionally, the coefficients A, B, and C cannot all be equal to zero.
The canonical form of a straight line equation in space is the simplified form of the equation, where the coefficients A, B, and C are all integers and the constant D is a real number. This form is useful for graphing and making calculations.
To convert an equation to its canonical form, you must first rearrange the terms to isolate the x, y, and z variables on one side of the equation, and the constant on the other side. Then, divide each term by the greatest common factor of the coefficients to simplify the equation and make the coefficients integers. Finally, divide both sides of the equation by the constant to make it equal to 1.
No, an equation can only have one canonical form. However, different equations can represent the same line in space, so they may have the same canonical form. It is important to note that the canonical form is not unique to a specific line, but rather to the equation itself.