How to Find Parametric Equations for a Line Perpendicular to Another Line?

Thread starter nameVoid
Start date Sep 19, 2010
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Lines Planes

In summary, the equation for a line in slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. Two lines are parallel if they have the same slope and will never intersect. A line is one-dimensional and extends infinitely in both directions, while a plane is two-dimensional and extends infinitely in all directions. To find the point of intersection between two planes, you can set their equations equal to each other and solve for the variables. A line and a plane cannot be parallel because they have different dimensions and will always intersect at some point.

Sep 19, 2010

nameVoid

Find the parametric equations find the line through point (0,1,2) that is perpendicular to the line x=1+t, y=1-t, z=2t

solution:
a=<a1,a2,a3>
1+t=a1s
1-t=a2s+1
2t=a3s+2

a1=1/s+t/2
a2=-t/s
a3=2t/s-2/s

<1/s+t/s,-t/s,2t/s-2/s>*<1,-1,2> = 0 =>t=1/2
P(3/2,1/2,1)
v=<-3/2,1/2,1>

also the latex does not seem to be working for me it does not update after an initial posting
x=3/2t, y=t/2+1, z=t+2

FAQ: How to Find Parametric Equations for a Line Perpendicular to Another Line?

What is the equation for a line in slope-intercept form?

The equation for a line in slope-intercept form is y = mx + b, where m represents the slope of the line and b represents the y-intercept, or the point where the line crosses the y-axis.

How do you determine if two lines are parallel?

Two lines are parallel if they have the same slope. In other words, the lines have the same steepness and will never intersect.

What is the difference between a line and a plane?

A line is a one-dimensional figure that extends infinitely in both directions, while a plane is a two-dimensional figure that extends infinitely in all directions. In other words, a line has length but no width or height, while a plane has both length and width but no height.

How do you find the point of intersection between two planes?

To find the point of intersection between two planes, you can set the equations of the planes equal to each other and solve for the variables. This will give you the coordinates of the point where the two planes intersect.

Can a line and a plane be parallel?

No, a line and a plane cannot be parallel. A line is a one-dimensional figure, while a plane is a two-dimensional figure, so they cannot have the same slope and will always intersect at some point.