Algebra Examples

Find the Plane Through (1,2,3),(2,5,6) Parallel to the Line Through (2,9,7),(3,3,3)
, , ,
Given points and , find a plane containing points and that is parallel to line .
First, calculate the direction vector of the line through points and . This can be done by taking the coordinate values of point and subtracting them from point .
Replace the , , and values and then simplify to get the direction vector for line .
Calculate the direction vector of a line through points and using the same method.
Replace the , , and values and then simplify to get the direction vector for line .
The solution plane will contain a line that contains points and and with the direction vector . For this plane to be parallel to the line , find the normal vector of the plane which is also orthogonal to the direction vector of the line . Calculate the normal vector by finding the cross product x by finding the determinant of the matrix .
Calculate the determinant of .
Tap for more steps...
Set up the determinant by breaking it into smaller components.
The determinant of is .
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by .
Multiply by .
Simplify the expression.
Tap for more steps...
Add and .
Move to the left of the expression .
Multiply by .
The determinant of is .
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by .
Multiply by .
Move to the left of the expression .
Multiply by .
Simplify by multiplying through.
Tap for more steps...
Apply the distributive property.
Multiply.
Tap for more steps...
Multiply by .
Multiply by .
The determinant of is .
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify each term.
Tap for more steps...
Multiply by .
Multiply by .
Move to the left of the expression .
Multiply by .
Add and .
Subtract from .
Solve the expression at point since it is on the plane. This is used to calculate the constant in the equation for the plane.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by .
Multiply by .
Multiply by .
Simplify by adding and subtracting.
Tap for more steps...
Add and .
Subtract from .
Add the constant to find the equation of the plane to be .
Simplify each term.
Tap for more steps...
Multiply by .
Multiply by .
Multiply by .
Enter YOUR Problem
Mathway requires javascript and a modern browser.