Here are three displacements, each in meters: d1 = 3.3i + 3.8j - 8.2k, d2 = -1.0i + 2.0j + 3.0k, and d3 = 4.0i + 3.0j + 2.0k. What is r = d1 - d2 + d3 ((a), (b) and (c) for i, j and k components respectively)? (d) What is the angle between r and the positive z axis? (e) What is the component of d1 along the direction of d2? (f) What is the component of d1 that is perpendicular to the direction of d2 and in the plane of d1 and d2?
The Attempt at a Solution
d) arccos(-9.2/13.3) = 133.82 degrees
also here, i was just wondering: what if they wanted the angle between r and y axis? would that be arcsin(4.8/13.3)? would x axis be arccos(8.3/13.3)?
E and F are my problems
E sounds like the definiton of dot prouct, so:
d1 dot d2 = (3.3)(-1) + (3.8)(2) + (-8.2)(3) = 20.3
it seems right to me...but i think its wrong
F sounds like cross product, so:
c = d1*d2 sin(phi), i can figure out the mags of d1 and d2, but i dont know what phi is