# Determine equation given 3 points and 2 lines

• euro94
In summary, the problem asks to find the equation for a line l2 that is perpendicular to another line l1, which passes through the points (-3,2,3) and (-8,10,6) and also passes through the point (7,49,25). To solve this, we need to determine the equation of l1 and use the dot or cross product to find the equation of l2.
euro94

## Homework Statement

Two coplanar lines l1 and l2 are perpendicular to each other, l1 passes through the points (-3,2,3) and (-8,10,6). Find the equation for l2 if it passes through the point (7,49,25)

## The Attempt at a Solution

determine the equation of l1 and use the dot or cross product?

What you have under "The attempt at a solution" is NOT an attempt at a solution! If you think you neeed to find the equation of the line l1, the find it! What is the equation of that line? What must the equation of any line through (7, 49, 25) look like?

## 1. How do I determine the equation given 3 points and 2 lines?

To determine the equation, first plot the 3 points on a coordinate plane. Then, use the slope formula to find the slope of each line. Next, use the point-slope formula to write the equations of the lines. Finally, solve the system of equations to find the intersection point, which is also the solution to the given equation.

## 2. What is the slope formula and how do I use it?

The slope formula is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on a line. To use it, simply plug in the coordinates of the two points and calculate the slope.

## 3. Can I use any 3 points to determine the equation of a line?

Yes, any 3 non-collinear points can be used to determine the equation of a line.

## 4. What is the point-slope formula and how do I use it?

The point-slope formula is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. To use it, simply plug in the coordinates of the point and the slope, and then rearrange the equation to the standard form, y = mx + b, where b is the y-intercept.

## 5. Can I determine the equation of a line if I only have 2 points?

Yes, you can determine the equation of a line with only 2 points. However, it is recommended to have at least 3 points to ensure accuracy and to check for any inconsistencies.

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