First slide

Introduction to 3-D Geometry

Question

In the $Δ ABC$ if $AB = \sqrt{2}, AC = \sqrt{20}$ , B = (3,2,0) and C = (0,1,4) then the length of the median passing through A is

Moderate

A

$\frac{3}{2}$
B

$\frac{9}{2}$
C

$\frac{3}{\sqrt{2}}$
D

$\frac{\sqrt{3}}{2}$

Solution

BC= $\sqrt{9 + 1 + 16} = \sqrt{26}$
a=BC,b=CA,c=AB
length of median= $\sqrt{\frac{2 b^{2} + 2 c^{2} - a^{2}}{4}}$

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