Can someone help me with this questions?.But please dont give me the answer.I just dont understand this lesson

Question

1)Find the cross product and show it is orthogonal to both u and v.

u=<-3,2,3>

v=<0,1,0>

 

2)Find the cross product and show it is orthogonal to both u and v.

     u=6k

     v=-i+3j+k

 

 

3)Find the area of the parrallelogram that has the two vectors as adjacent sides

 

u=2i+4j+6k

v=i+k

 

4)Find the cross product of the unit vectors

                   J×k

                 i j k

                0 1 0

                0 0 1

 

 

THE LESSON IS CROSS PRODUCT OF TWO VECTORS

Answer 1

The vector cross product is defined as

 

u x v= (u_yv_z-u_zv_y)i + (u_zv_x-u_zv_z)j + (u_xv_y-u_yv_x)k where u_x is the x component of U

 

u=u_xi+u_yj+u_zk  and likewise for v

 

1. you were given the components of u and v using the above definition of the cross product calculate the vector a=uxb. The next step is to recall that if two vectors are orthogonal then one is perpendicular to the other and the dot product is zero. So you have to show that a• u =0 and a•v =0

 

Does this help get you started?

Jim