A unit normal vector to the plane containing the points (1,0,0), (0,1,0), (0,0,1) (possible solutions below) ?
a. (29) ^-1/2 <4, 2, -3>
b. (21) ^-1/2 <2, -1, 4>
c. (14) ^-1/2 <1, 3, -2>
d. (17) ^-1/2 <2, 3, 2>
e. <1, 1, 1>
or is it none of these?
2 Responses
Carl M
13 Mar 2010
Tom
13 Mar 2010
<1,1,1> is a normal vector. You can see this by taking two vectors in the plane say <1,-1,0> and <1,0,-1> and finding their cross product which is <1,1,1>. Unfortunately this is not a unit vector. You would have to divide each component by radical 3 to get that. The answer is none of these.
From visualizing the problem, I’d go with e, (1, 1, 1).
The plane you’ve described makes a three sided symetrical pyramid with the apex at the origin. The point (1.1.1) is directly "below" the origin, and thus normal to the base.
I edit my answer to agree with Tom (the answer below this). (1,1,1) is NOT a unit vector, although this is the kind of error that a teacher could be likely to make. If this is a multiple choice, go with e. If this is a short answer, note that (1,1,1) is normal to the plane, and offer Tom’s properly scaled version as an alternative.