Find the distance between the following pairs of points:

Question

CASE_STUDIESDistance Formula in Three Dimensional Space4 sub-questions

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Find the distance between the points P(1, –3, 4) and Q (– 4, 1, 2).

Show that the points P (–2, 3, 5), Q (1, 2, 3) and R (7, 0, –1) are collinear.

Are the points A (3, 6, 9), B (10, 20, 30) and C (25, – 41, 5), the vertices of a right angled triangle?

Find the equation of set of points P such that PA² + PB² = 2k², where A and B are the points (3, 4, 5) and (–1, 3, –7), respectively.

Show that the points (–2, 3, 5), (1, 2, 3) and (7, 0, –1) are collinear.

Verify the following: