Thursday

October 2, 2014

October 2, 2014

Posted by **J** on Saturday, May 5, 2012 at 12:28pm.

- Calculus -
**Reiny**, Saturday, May 5, 2012 at 4:04pmI think you posted this before, and probably got no response.

You asked for "the" line parallel to the plane

2x+6y+4z = 1.

There is no unique line.

Think of the floor of your kitchen as 2x+6y+4z = 1 and you have a table whose top is parallel to the floor and contains the point (3,2,1).

Laying down a ruler would be a line parallel to the plane and passing through the point.

How many such positions could you choose ?

a normal to your given plane is (2,6,4) or (1,3,2)

so any vector whose dot product with the above normal would be parallel to the plane

e.g. (-5,1,1)∙(1,3,2) = -5+2+3 = 0

and (1,-1,1)∙(1,2,3) = 1-3+2 = 0 are just two such vectors

let's take (-5,1,1)

so the equation of one such line is

x = 3 -5t

y = 2 + t

z = 1 + t

- Calculus -
**J**, Sunday, May 6, 2012 at 1:34amthank you :)

**Answer this Question**

**Related Questions**

Calculus grade 12 - Determine an equation for the line parallel to 2x + 6y + 4z...

Calculus grade 12 - Determine an equation for the line parallel to 2x + 6y + 4z...

Calculus - determine an equation for each plane a) contains the point A(6,2,3), ...

Calculus - determine an equation for each plane a) contains the point A(6,2,3), ...

math - find the equation of a line that is parallel to the line x= -1 and ...

MATH! - What type of lines have a slope of zero? Write the equation of a line ...

math - The equation of line AB is y = 2x + 4. Write an equation of a line ...

math - The equation of line AB is y = 2x + 4. Write an equation of a line ...

Math - Find the equation of the line that contains the point (-4,-6) and is ...

calculus - find an equation for the line with the given properties. express the ...