A ball travels with velocity given by [2, 1] with wind blowing in the direction given by [3, -4] with respect to some co-ordinate axes. What is the size of the velocity of the ball in the direction of the vind?
v = [2, 1] b = [3, -4]
I did as follows:
projection of v onto b = (v.b.)/ |b|^2
v.b = 2 , |b|^2 = 25
Therefore, the projection of v onto b = 2 / 25. In other words, the scalar projection is 2/25, right? Therefor the answer should be 2/25.
However, when I then calculated the absolute value by multiplying 2/25 * [3, -4] --> [6/25, -8/25] --> |b| = square root((6/25)^2 + (-8/25)^2) --> |b| = 2/5.
Which then gives me then answer 2/5, how come the scalar projection and the absolute value differs? Shouldn't the scalar projection be the length of, in this case, the size of the velocity of the ball in the direction of the vind? But the right answer is 2/5...