The number of values of 'k' for which the points (-4,9,k), (-1,6,k), (0,7,10) form a right-angled isosceles triangle is
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When dealing with geometric conditions in 3D, first calculate the squared distances between the points. This avoids dealing with square roots. Then, apply the conditions (e.g., two sides equal for isosceles, Pythagoras' theorem for right-angled) to the squared lengths.