Please explain to me why R = (A x B) * C is equal to 0?

Question

A = 30.0m, 30 degrees

B = 40.0m, 125 degrees

C = 35.0m, 300 degrees

All vectors are in an XY graph.

For me, I got R = (A x B) * = 1.

R = (A x B) * C

=(i x j) * C

=k * k

=(1)(1)cos 0 = 1

I can see that (i x j) becomes perpendicular to C which makes a 90 degree angle and that when A * B that has a 90 degree angle is therefore equal to zero.

I'm confused...is it a 1 or 0? or neither? :-P

Answer 1

All three vectors are in xy plane. If you take cross product of two vectors, then the result is perpendicular to both vectors. In other words, the result is perpendicular to the plane containing the two vectors.

Therefore A X B is perpendicular to xy plane.

C is in xy plane.

Therefore, A X B is perpendicular to C.

If you take dot product of two perpendicular vectors, then the result is zero.

Therefore, (A X B).C = 0

Note that I have not used the numbers you have given because the numbers do not matter. So long all three vectors are in the same plane, (A X B)*C will be zero.

You have written (i X j)*C = k*k. This is wrong because C is NOT along z axis. Therefore, you should not use k for C.

Ans: zero

Answer 2

A=  a1 cos30 i + a2 sin 30 j

B= b1 cos125 i + b2 sin 125 j

C= c1 cos300 i + c2 sin300 j

(AxB) = |A||B| sin95 k

(AxB) * C = (|A||B| sin95 k) (c1 cos300 i + c2 sin 300 j)

(AXB)*C= 0, since i*k and j*k is zero.

so....it's zero.