... 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 ...

... 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 ...

... Again, we need a point a vector perpendicular to our plane. We know, that the cross-product of two vectors a and b is perpendicular to both a and ...

... as well as the equation of the normal plane to the ... normal) to T(t). To ﬁnd the third vector, B(t ... of T and N. The cross-product of two vectors is perpendicular ...

... is 1 - 4 + 3 = 0; hence, the planes are orthogonal. ... and (1, -2, 3) to get a vector perpendicular to ... 1, -2) is also perpendicular to both vectors (dividing each ...

... 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 ...

... so that when it hits the ground, it is 4410 m directly below the plane! ... the vector from the axis of rotation to the application point and the force vector. ...