The figure below shows two vectors a and b in R³ that are in the xy-plane. Suppose ||a|| = 4, ||b|| = 3, and the angle between the two vectors is 50 degrees.
a. The dot product of these vectors is a · b = . You should be able to determine the sign of a · b without making any calculations.
b. The cross product a x b points in the same direction as the vector . You should be able to determine this without making any calculations.
c. The length of a x b is ||a x b|| = .
d. The cross product a x b is .
e. The area of the triangle formed by a and b is .