vector `veca` lies in the xy plane, has a magnitude of 18 units, and points in a direction `250^(@)` from the positive direction of the x axis. Also, vector `vecb` has a magnitude of 12 units and points in the positive direction of the z axis. What is the vector product `vecc=vecaxx vecb` ?

Options

A. 30
B. 35
C. 40
D. 45

Answer

D

Explanation

`vec(A) = (5 cos 120) hat(i) + (5 sin 120)hat(j)= (-5)/(2) hat(i) + (5 sqrt3)/(2) hat(j)`
`vec(B) = 9 hat(k)`
`vec(A) xx vec(B) = |(hat(i),hat(j),hat(k)),((-5)/(2),(5 sqrt3)/(2),0),(0,0,9)|= - ((-45)/(2)) hat(j) + ((45 sqrt3)/(2)) hat(i)`
`vec(A) xx vec(B)= (45 sqrt3)/(2) hat(i) + (45)/(2) hat(j)`
`|vec(A) xx vec(B)|= sqrt(((45 sqrt3)/(2))^(2) + ((45)/(2))^(2))= (45)/(2) sqrt4= 45`