Can't do this stupid question (1 Viewer)

[jinglebells1464646]

I don't know how to do C. Here my working. I used the fact that "modulus of cross product of two vectors = area of the parallelogram enclosed by those vectors"
The base/floor/subscript vector in the projection expressions is the arbitrarily chosen vector (1,1,0) which has a z=0 coordinate since the question states we want to project onto the x-y plane. Then I apply the cross product formula and blah blah blah and I end up with the result of a zero vector for area which is a contradiction. I even verified my calculations using Symbolab Linear Algebra Calculator and it's not working. the answer is supposed to be 8 units.

 

[Drongoski]

Is the area 8, by any chance?

 

[Luukas.2]

It looks to me like you are trying to project onto the vector i + j to get onto the xy-plane.

Any plane can be defined in terms of a vector normal to it - in the case of the xy-plane, one such unit normal vector is k. To project a vector v onto that plane, the projection of v onto the normal vector must be subtracted from the original vector.

So, the projection of v onto the xy-plane is v - proj_kv.

PS: @jimmysmith560, this thread belongs in the Extension 2 forum, 3D vectors have yet to be added to the extension 1 syllabus.