Question:
11. If the extremities (end points) of a diagonal of a square are (1,–2,3) and
(2,–3,5) then find the length of the side of square.
Answer:
Let a is the length of the side of a square.
Given, the diagonal of a square are (1,–2,3) and (2,–3,5)
Now, length of the diagonal of square = √{(1 - 2)2 + (-2 + 3)2 + (3 - 5)2 }
= √{1 + 1 + 4}
= √6
Again length of the diagonal of square is √2 times the length of side of the square.
=> a√2 = √6
=> a√2 = √3*√2
=> a = √3
So, the length of side of square is √3 unit
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