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Applications of Dot Product

If the length...

Question

If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be

equal to the side of cube

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\sqrt{3}

times the side of the cube

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\frac{1}{\sqrt{3}}

times the side of the cube

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impossible to find from the given information

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Solution

The correct option is A equal to the side of cube
DF,AG and CE are body diagonals of cube Let the side of cube be a.
Therefore, body diagonal is a $\sqrt{3}$
Circum radius for equilateral triangle $\frac{s i d e}{\sqrt{3}}$
Therefore, $\frac{a \sqrt{3}}{\sqrt{3}} = a$
The answer is well described in the figure itself

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If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be

The correct option is A equal to the side of cubeDF,AG and CE are body diagonals of cube Let the side of cube be a.Therefore, body diagonal is a √3Circum radius for equilateral triangle side√3Therefore, a√3√3=aThe answer is well described in the figure itself