Two vectors of magnitudes 20cm and 10cm make angles of 120o and 150o respectively with x-axis in the xy plane. Find the magnitude and direction of their cross product.
Answers
The resultant of the given two vectors can easily be figured out just by resolving the vectors into x and y components
Resolving A vector, we get 10cos(30°) and 10sin(30°) , which is equal to 5√3 and 5 along x and y axis respectively
Now resolving B vector, we get -20cos(30°)[carries negative sign as it is along negative X-axis] and 20sin(30°), which is equal to -10√3 and 10 along X and Y axis respectively
Equating the resolved vectors that are along x axis, we get -5√3 ,which can be assigned to Rx (just for our convenience)
Equating the resolved vectors that are along Y axis, we get 15,which can be taken as Ry
Thus the X and Y components of the resultant vector has been found out
Futher Pythagoras theorem can be used to calculate the resultant vector ‘R’ using its X and Y components ( i.e Rx and Ry)
Therefore ‘R’ vector =√(Rx^2 + Ry^2)
=√(5√3^2 + 15^2) = √(225+75) = √300
=10√3 = 17.32
The magnitude of the resultant vector is 17.32