Question

Consider a triangle formed by connecting the three points: (0 0 0), (1 0 0), (1 1 1). a. Find the vector which is perpendicular to the surface of this triangle, AND has a positive z-direction?

Answer 1

=k−j or (0 -1 1)

Explanation:

The Vector or Outer Product two vectors, say →x&→y, is

denoted by →x×→y, is a perpendicular vector to the plane containing them.

The given pts. A (0 0 0), B (1 0 0), C (1 1 1) lie in a

plane ABC.

As suchType equation here., the vectors (→(AB ) )and (→AC ) are members, ∈ of the plane ABC

That is □(→(AB )×(→AC)) to the plane ABC

(→(AB ) )=(1-0,0-0,0-0)=(1,0,0)

(→(AC ) )=(1-0,1-0,1-0)=(1,1,1)

(→(AB )×(→AC= (0i -j k)

=k−j

Which is in the positive Z direction