Write the parametric equation of the line

In summary, the problem asks to find values for a, b, and c such that the point (a,b,c) is on the line passing through the points (3,-4,0) and (2,-2,3) and satisfies the equation a + b + c = 7. The suggested approach is to write the parametric equation of the line and use it to solve for t, then find the corresponding values for a, b, and c.
  • #1
Whiz
20
0

Homework Statement



Given a + b + c = 7, find a, b and c such that the point (a,b,c) lies on the line passing through the points (3,-4,0) and (2,-2,3)

a =
b =
c =

Homework Equations



None

The Attempt at a Solution



My instructor didn't go through this portion and I was wondering if I could get a little help.
The way I understand the question is that there is a point between (3,-4,0) and (2,-2,3), such that they equal 7. I'm not sure how to go about this question.

Any hints?

Thanks in advance.
 
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  • #2


If you meant ax+by+cz=7 and you want to find a,b,c such that (3,-4,0) and (2,-2,3) lie on this plane, then what would happen if you substituted a point (x0,y0,z0) which lies on the plane, into the equation of the plane?
 
  • #3


rock.freak667 said:
If you meant ax+by+cz=7 and you want to find a,b,c such that (3,-4,0) and (2,-2,3) lie on this plane, then what would happen if you substituted a point (x0,y0,z0) which lies on the plane, into the equation of the plane?

Hmm but I typed the question exactly the way it is.

And I'm not sure what you mean by substituting (x0,y0,z0)
into the equation of the plane.
 
  • #4


Write the parametric equation of the line, so you have expressions for x, y, and z in terms of t. Then set x + y + z = 7, figure out t and hence the required point.
 

1. What is a parametric equation?

A parametric equation is a mathematical expression that describes the relationship between two variables, typically represented as functions of a third variable called a parameter. In the context of lines, the parametric equation represents the coordinates of points on the line in terms of a parameter t.

2. How do you write the parametric equation of a line?

The parametric equation of a line can be written as x = x0 + at and y = y0 + bt, where (x0, y0) is a point on the line and a and b are the direction numbers of the line. This equation can also be written in vector form as r = r0 + t v, where r0 is the position vector of a point on the line and v is the direction vector of the line.

3. What is the significance of the parameter in the parametric equation of a line?

The parameter in the parametric equation of a line represents the variable t, which determines the position of points on the line. As t varies, the coordinates of points on the line change, and the entire line is traced out. The parameter allows for a more flexible and concise representation of a line compared to the standard slope-intercept form.

4. How can the parametric equation of a line be used to find the slope and y-intercept?

The slope of a line in parametric form is given by b/a, where a and b are the direction numbers. The y-intercept can be found by substituting t = 0 into the equation and solving for y. However, it should be noted that the concept of slope and y-intercept may not be as straightforward in parametric form compared to the standard form.

5. Can the parametric equations of two lines be used to determine if they intersect?

Yes, the parametric equations of two lines can be used to determine if they intersect. By setting the two equations equal to each other and solving for t, the parameter at which the lines intersect can be found. If there is a solution, then the lines intersect at that point. If there is no solution, then the lines are parallel and do not intersect.

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