Finding cross product of two vectors a,b

[mmattson07]

Homework Statement

A vector of magnitude 17 units and another vector of magnitude 7.4 units differ in directions by 27°. Find (a) the scalar product of the two vectors and (b) the magnitude of the vector product ×.

Homework Equations

Right-hand rule, a*b=abcos(theta), A x B= absin(theta)

The Attempt at a Solution

Dot product => a*b= (17)(7.4)(cos(27))= 112.089

Just not quite sure on how to do the cross product. The right hand rule gives me a vector pointing straight up the z axis when sweeping into b but not sure what values to plug into absin(theta) Thanks.

 

[mmattson07]

Hm. It seems the answer is just 17(7.4)(sin(27). Not sure geometrically why this is the case though.