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Equation of a Plane : Intercept Form

8. Prove that...

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8. Prove that the points (1, 1, 1), (-2, 4, 1), (- 1, 5, 5) and (2, 2, 5) are thesquare.

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Q. Prove that the points

(2, - 2), (8, 4), (5, 7),

(- 1, 1)

are the angular points of a rectangle.

\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{5}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}}

= 2

\frac{1}{3 - \sqrt{8}} - \frac{1}{\sqrt{8} - \sqrt{7}} + \frac{1}{\sqrt{7} - \sqrt{6}} - \frac{1}{\sqrt{6} - \sqrt{5}} + \frac{1}{\sqrt{5} - 2} = 5

Q. Prove that the points

(4, 5, - 5), (0, - 11, 3)

(2, - 3, - 1)

2 {tan}^{- 1} \frac{1}{5} + 2 {tan}^{- 1} \frac{1}{8} + {sec}^{- 1} \frac{5 \sqrt{2}}{7} = \frac{π}{4}

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