# 3d – New coordinate of another point after rotating one point on \$S^2\$?

As we rotate $$p_a = (x_a, y_a, z_a)$$ to $$p_b = (x_b, y_b, z_b)$$ (both are known), how can we find the the new location of $$p_c = (x_c, y_c, z_c)$$ after this rotation? Can we instead find out the new location of $$overrightarrow{p_a p_c}$$ after this rotation? Thanks in advance.