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Show that the points (1, 2, -2), (2, 3, ...

Show that the points (1, 2, -2), (2, 3, -4) and (3, 4, -3) form a right angled triangle.

Text Solution

Verified by Experts

Let A(1, 2, -2), B(2, 3, -4) and C(3, 4, -3) be given points
`AB = sqrt((2-1)^(2)+(3-2)^(2)+(-4+2)^(2))=sqrt(6)` units
`BC = sqrt((3-2)^(2) +(4-3)^(2) + (-3+4)^(2)) =sqrt(3)` units
and `AC = sqrt((3-1)^(2) +(4-2)^(2)+(-3+2)^(2))=sqrt(9)` units
Now `AB^(2) +BC^(2)=AC^(2)`
Hence, the given points form a right angled triangle.
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