Monday

December 22, 2014

December 22, 2014

Posted by **J** on Saturday, May 5, 2012 at 12:44pm.

- Calculus -
**MathMate**, Saturday, May 5, 2012 at 11:15pmIf the line

L: [x,y,z] = [-2,6,5] + t[3,2,-1]

lies in the plane

P: 3x - 4y + z + 25 = 0

Then both of the following must be true

1. [-2,6,5] must lie in the plane.

Check: 3(-2)-4(6)+5+25=0

so [-2,6,5] lies in the plane

2. the vector <3,2,-1> must be orthogonal to the vector <3,-4,1> of the plane.

Check: <3,-4,1>.<3,2,-1>=9-8-1=0

So the line is perpendicular to the normal of the plane.

Therefore the line lies in the plane.

Alternatively, locate any two points on the line and show that they both lie in the plane.

- Calculus -
**J**, Sunday, May 6, 2012 at 1:54amthank you!

- Calculus -
**MathMate**, Sunday, May 6, 2012 at 4:01amYou're welcome!

**Answer this Question**

**Related Questions**

Geometry - 4.Determine which point does not lie on the graph of the line y=x-3 a...

Calculus - Show that the vectors (-1,2,3), (4,1,-2) and (-14,-1,16) do not lie ...

calculus - I have two questions please. 1. find an equation for the line with ...

calculus - I have two questions please. 1. find an equation for the line with ...

Algebra 2 - 1. Give 3 points that lie on the line 4x-y=6. 2. Give 3 points that ...

Algebra 2 - 1. Give 3 points that lie on the line 4x-y=6. 2. Give 3 points that ...

Algebra 2 - 1. Give 3 points that lie on the line 4x-y=6. 2. Give 3 points that ...

Calculus - Verify please and thank you~ Does the line (x-7)/3=(y+8)/6=(z+4)/5 ...

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

Math- intersection of planes - Show that the line [x,y,z]=[10,5,16]+t[3,1,5] is ...