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Find the equation for the plane passing through the heads of the three given vectors

(2, 2, 0)

(−1, 2, 1)

(1, 1, 4)

Is this just another way of asking what is the plane passing through these points, or does "through the heads" mean something different.

Thanks.

Luke
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2 Answers2

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Simply ensure that all three points are on the plane. A point and two direction vectors are required to define a plane.

By stating "head of the three vectors", this implies that the vectors are coming from the origin (with the tail at 0,0,0). The "head" essentially represents a point on the plane.

user264985
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  • Alright, so just to check the answer would be 2a - 2b + 6c - 24 = 0? – Luke Nov 27 '15 at 04:40
  • x+11y-3z-24=0, remember you need to be able to satisfy ALL of the three points – user264985 Nov 27 '15 at 04:48
  • useful calculator with explanation at bottom http://keisan.casio.com/exec/system/1223596129 – user264985 Nov 27 '15 at 04:49
  • the calculator is giving a different answer than what you said, could you walk me through the steps of how you are getting it? – Luke Nov 27 '15 at 07:11
  • my bad, answer's x+11y+3z-24=0, calculator is correct – user264985 Nov 27 '15 at 12:22
  • first step: find any two direction vectors using the given three points. then, find the cross product of those direction vectors. then find the dot product of the cross product (found earlier) with a point on the plane (this is your D value). The coefficients of your cross product are your A, B, C respectively. The form is Ax + By + Cz - D = 0 – user264985 Nov 27 '15 at 12:28
  • Ah, thanks. I got it now. – Luke Nov 27 '15 at 21:51
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It should just mean through the three points, although it does seem to be a rather bizarre way to phrase it.

Luke Hamblin
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