With respect to the origin O, the position vectors of the points A, B,C and D are

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With respect to the origin O, the position vectors of the points A, B,C and D are given by

a. In the case where ABC is a right angle, find the possible values of the constant m.

b. In the case where D is the midpoint of the line BC, find the value of the constant m.

c. In the case where m = −5, find whether the lines AB and CD intersect.

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