How do I know if two planes are parallel?

**terrorsquid** · October 15th 2011, 07:36 AM

Determine whether the given planes are parallel:

$4x-y+2z=5$
$7x-3y+4z=8$

I think I can find a vector that is parallel to each plane, but I am not quite sure how to compare the vectors that I find. Here is what I have done:

I tried to find 2 points on each that satisfied the equations then found the vector joining the two points...

$4(1)-(-1)+2(0) = 5 \rightarrow (1,-1,0)$

$4(0)-(-1)+2(2) = 5 \rightarrow (0,-1,2)$

$\vec{v} = <1,0,-2>$

$7(0)-3(0)+4(2) = 8 \rightarrow (0,0,2)$

$7(1)-3(1)+4(1) = 8 \rightarrow (1,1,1)$

$\vec{r} = <-1,-1,1>$

How do I check to see if $\vec{v}$ and $\vec{r}$ are parallel?

Can I solve this using an augmented matrix maybe?

**Plato** · October 15th 2011, 07:45 AM

Originally Posted by terrorsquid

Determine whether the given planes are parallel:
$4x-y+2z=5$
$7x-3y+4z=8$

Two planes are parallel if and only if their normals are parallel.

Are $<4,-4,2>~\&~<7,-3,4>$ parallel?

**terrorsquid** · October 15th 2011, 07:58 AM

That's my question, I don't know how to tell if two vectors are parallel or not.

Surely the vectors that lie on each plane could be compared?

**Plato** · October 15th 2011, 08:08 AM

Originally Posted by terrorsquid

That's my question, I don't know how to tell if two vectors are parallel or not. Surely the vectors that lie on each plane could be compared?

You really should not try these questions until you master the fundamentals.

Two vectors are parallel if they are non-zero scalar multiples of one another.

Thread: How do I know if two planes are parallel?

LinkBack

Thread Tools

Display

How do I know if two planes are parallel?

Re: How do I know if two planes are parallel?

Re: How do I know if two planes are parallel?

Re: How do I know if two planes are parallel?

Similar Math Help Forum Discussions

Lines through/parallel to planes?

Parallel planes and intersecting planes

How to tell if three planes are parallel or not

Vector parallel to both planes?

Distance between two parallel planes

Search Tags