Question

Find an equation for the plane passing through the point (0,4,1) which is parallel to the vectors <1,2,3> and <0,-1,1>.

Could you please teach me do this question? Thank you very much.

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- Dec 12th 2006, 04:22 AMJenny20planes in 3-space
Question

Find an equation for the plane passing through the point (0,4,1) which is parallel to the vectors <1,2,3> and <0,-1,1>.

Could you please teach me do this question? Thank you very much. - Dec 12th 2006, 04:42 AMCaptainBlack
- Dec 12th 2006, 05:01 AMSoroban
Hello, Jenny!

Quote:

Find an equation for the plane passing through the point P(0,4,1)

which is parallel to the vectors**u**= <1,2,3> and**v**= <0,-1,1>.

Since the plane is parallel to**u**and**v**,

. . its normal vector**n**is*perpendicular*to both**u**and**v**.

Then**n**is the*cross product*of**u**and**v**.Code:`| i j k |`

n = | 1 2 3 | = 5i - j - k = <5,-1,-1>

| 0 -1 1 |

You have a point P(0,4,1) and normal vector**n**= <5,-1,-1>

You can write the equation: .5(x - 0) - 1(y - 4) - 1(z - 1) .= .0

- Dec 12th 2006, 06:13 PMJenny20
Thank you very much Soroban. Your explanation is very clear to me. :)

Also, Thank you very much CaptainBlack.