If centroid of the tetrahedron OABC- where A-B-C nbsp-are given by -a- 2- 3-1- b- 2- and -2- 1- c- respectively be nbsp-1- 2- -1- then distance of P-a-b-c- nbsp-from origin is equal to None of these

The correct option is C Centroid ≡(∑ x/4,∑ y/4,∑ z/4 )=(1,2, 1) ⇒ a=1,b=5,c= 9;∴√(a^2+b^2+c^2)=√(107). ...

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Standard XII

Mathematics

Centroid of a Tetrahedron

If centroid o...

Question

If centroid of the tetrahedron OABC, where A,B,C are given by (a, 2, 3),(1, b, 2) and (2, 1, c) respectively be (1, 2, -1), then distance of P(a,b,c) from origin is equal to

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None of these

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Solution

The correct option is A

Centroid $\equiv (\frac{\sum x}{4}, \frac{\sum y}{4}, \frac{\sum z}{4}) = (1, 2, - 1)$
$\Rightarrow a = 1, b = 5, c = - 9; ∴ \sqrt{a^{2} + b^{2} + c^{2}} = \sqrt{107}$ .

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If centroid of the tetrahedron OABC, where A,B,C are given by (a, 2, 3),(1, b, 2) and (2, 1, c) respectively be (1, 2, -1), then distance of P(a,b,c) from origin is equal to

The correct option is A Centroid ≡(∑x4,∑y4,∑z4)=(1,2,−1) ⇒a=1,b=5,c=−9;∴√a2+b2+c2=√107.

The correct option is A

Centroid $\equiv (\frac{\sum x}{4}, \frac{\sum y}{4}, \frac{\sum z}{4}) = (1, 2, - 1)$
$\Rightarrow a = 1, b = 5, c = - 9; ∴ \sqrt{a^{2} + b^{2} + c^{2}} = \sqrt{107}$ .