Find the intersection point for x = -5 + 8t, y = 1 + 10t, z = 9 + 8t ; -2x + 8y + 8z = 10

MHB
Thread starter aa1604962
Start date Mar 23, 2020
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Intersection Point

In summary, the intersection point for the given equations is (-2, 4, 10). To find the intersection point for two or more equations, you can use the substitution method or the elimination method. The equation -2x + 8y + 8z = 10 represents a plane in three-dimensional space and can be written in vector form. The intersection point represents the point where the given lines and plane intersect in three-dimensional space and can be used to determine the exact location where they intersect. The concept of intersection points has various real-life applications in fields such as physics, engineering, and economics.

Mar 23, 2020

aa1604962

Find the intersection.

x = -5 + 8t, y = 1 + 10t, z = 9 + 8t ; -2x + 8y + 8z = 10

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Mar 23, 2020

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MHB

aa1604962 said:

Find the intersection.

x = -5 + 8t, y = 1 + 10t, z = 9 + 8t ; -2x + 8y + 8z = 10

Start by replacing x with -5 + 8t, y with 1 + 10t, and z with 9 + 8t, in your plane.

1. What is the intersection point for the given equations?

The intersection point for the given equations is (-5, 1, 9).

2. How do you find the intersection point for two or more equations?

To find the intersection point for two or more equations, you need to solve the equations simultaneously. This can be done by substituting one variable into the other equations until you have a single variable equation, which can then be solved to find the value of that variable. Repeat this process for each variable until you have values for all variables, which will give you the intersection point.

3. Can there be more than one intersection point for two or more equations?

Yes, there can be more than one intersection point for two or more equations. This can happen when the equations are not independent and represent the same line or plane in space.

4. What does the value of t represent in the given equations?

The value of t represents the parameter or variable used to represent the position of a point on the line or plane defined by the equations. It can be thought of as the time or distance traveled along the line or plane.

5. Can the given equations be solved using other methods besides substitution?

Yes, the given equations can also be solved using elimination or graphing methods. Elimination involves manipulating the equations to eliminate one variable at a time, while graphing involves plotting the equations on a graph and finding the point of intersection visually.