... 5. If two planes are parallel, then a normal vector to one is a normal vector to the other as well: The plane M' is defined by the vectors u and v ...

... z - 1) = 0 x - y - z = 0 ===== equation of the tangent plane). (b) Consider an arbitrary point R(x ... Line PR is parallel to the normal vector N = (1, -1 ...

... Now, if our plane is parallel to both N(0) and B ... be perpendicular to T(0), as these three vectors are pairwise ... for all t. So, we have a vector perpendicular to ...

...Vectors PQ and PR then must be parallel to our ... Now we have a vector perpendicular to our plane and can ... intercept, and that's z = 1. So, the plane goes parallel ...

... Thus, a plane is determined by one point in it and the normal vector to it. Given two vectors u and v, we know that their cross-product uxv is perpendicular ...

... c and the surface f x , y on the xy plane. ... The curl is a cross product between the vector field F ... A cross product between two parallel vectors is zero. ...

... c) we know that two vectors u and v are perpendicular, if uv = 0. ... with ||u|| = 2 => u12 + u22 + u32 = 4. now if the vector lies in yz-plane, we have u1=0. ...

... of the proton r = the unit vector from charge to the point of interest (the dot). Since both of this vectors are on the xy plane, the cross product of them ...