Posted by **Brandon** on Monday, September 17, 2012 at 10:51pm.

Find a linear function whose graph is the plane that intersects the xy-plane along the line y=2x+2 and contains the point (1,2,2).

- Calculus -
**Steve**, Tuesday, September 18, 2012 at 10:53am
a little vector analysis makes this relatively easy. Find two points B and C on the line. Let A=(1,2,2)

Form vectors **AB** and **AC**. These two vectors lie in the desired plane. Let **n** be the normal to the plane.

**n** = **AB** × **AC**

**n**•(**v**-**A**) = 0 is the desired plane.

So, pick any two points on the line, say B=(0,2,0) and C=(1,4,0)

AB = -i -2k

AC = 2j -2k

n =

| i j k |

|-1 0 -2 |

| 0 2 -2 |

= 4i -2j + 2k

4i -2j + 2k • (x-1)i + (y-2)j + (z-2)k = 0

2x-y+z = 2

For a fuller explanation, see

www.jtaylor1142001.net/calcjat/Solutions/VPlanes/VPPtLine.htm

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