The problem starts out with 2 vectors given: R= -3i+j-2k S= 2i+5j-4k I was asked

Question

The problem starts out with 2 vectors given:
R= -3i+j-2k
S= 2i+5j-4k
I was asked for the magnitudes, the scalar product of R*S, the angle between R and S, the component of R in the direction of S, and the angle between S and the positive y-axis. I solved everything except the angle between S and the positive y-axis so that is what I need help with. I do have the answer to it though.
Answers:
Magnitude R= 3.74
Magnitude S= 6.71
R*S= 7
Between R and S= 73.8 degrees
Component of R in S direction= 1.04
~~~~Angle between S and positive y-axis= 41.8 degrees

Explanation / Answer

The given vector S = 2i + 5j - 4k and the unit vector along y axis is y = j then the scalar product is         S . y = Sy cos here    S = (2^2 + 5^2 + 4^2 = 6.7 and y = 1 now        (2i + 5j - 4k) . (j) = (6.7)(1) cos          5 = 6.7 cos therefore the angle between them is      = cos^-1 ( 5/6.7) = 41.8 deg

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