Question

You are looking down at a map. A vector u with IuI=2 points north and a vector v with IvI= 9 points northeast. The crossproduct u x v points in which direction? *Help please, I just started calc3 and have no clue

Answer 1

The magnitude of a cross product is defined as |u||v|sin a, where a is the angle between the two vectors. In your case, the magnitudes of u and v are given as 2 and 9 respectively. The angle between them is given as well (The angle between North and Northeast is 45 degrees). Thus the magnitude of your new vector (the cross product of u and v) is:\[(2)(9)\sin (\pi/4)\approx12.7\]Now all we need is the direction of this new vector. By definition, the direction of a cross-product is given by the "right-hand" rule. In this case, since you are looking down at the map, the right-hand rule would give a vector pointing down, into the page.

Answer 2

Thanks a lot for your help. It makes more sense now :D

Answer 3

To see this, point the fingers of your right hand in the direction of u. Next, curl your fingers in the direction of v, going the way of the smaller of the two angles between them (the angle between u of v is 45 degrees or360-45=315 degrees; you want to curl in the direction of the 45 degrees i.e., the shorter distance). The direction of u x v will be the direction your thumb points.

Answer 4

np :)