Aflat mirror is rotated 21 ∘ about an axis in the plane of the mirror. part a what is the angle change of a reflected light beam if the direction of the incident beam does not change?

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

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