Two vectors p and q of magnitude 5 and 3 units respectively are inclined at an angle of 30o to each other.calculate the resultant i) in the direction of q ii) perpendicular to the direction of q b) hence calculate magnitude of the resultant and the angle with the direction of Q

Answer 1

Let's put q on the x axis
then p is 30 degrees above the x axis
In the direction of q (x direction):
3 + 5 cos 30 = 3 + 4.33 = 7.33
in the direction perpendicular to q (y axis) :
5 sin 30 = 2.5
|R| = sqrt (7.33^2 + 2.5^2) = sqrt(60) = 7.74
tan angle above x axis = 2.5 / 7.33 = 0.341
angle = 18.8 degrees