abdo799 said:Homework Statement
find the vector with magnitude 5 and perpendicular to 3i-2j+4k and 4i-3j-kThe Attempt at a Solution
lets name the vector component x for the i y for the j and z for the k
i got three equation
1- x^2+y^2+z^2=25 ( magnitude)
2-3x-2y+4z=0
3-4x-3y-z=0 (2, 3 from dot product by the 2 given vectors)
i am supposed to solve those simultaneously, but i can't do it
Linear equations are equations in which the variables have an exponent of 1, meaning the highest degree of any term is 1. This results in a graph that is a straight line. Non-linear equations, on the other hand, have variables with exponents greater than 1, resulting in a curved graph.
The most common method for solving a system of linear equations is by using the substitution method. This involves isolating one variable in one of the equations and then substituting its value into the other equation. The resulting equation can then be solved for the remaining variable.
Yes, a system of non-linear equations can have more than one solution. Depending on the complexity of the equations, there can be multiple points of intersection between the graphs of the equations, resulting in multiple solutions.
Finding the solution to a system of equations can help to solve real-world problems and make predictions. These equations can represent relationships between different quantities, and finding their solution can provide valuable information and insights.
Yes, it is possible to solve a system of equations with more than two variables. However, the number of equations must be equal to or greater than the number of variables in order to find a unique solution. Otherwise, there will be an infinite number of solutions.