First slide

Introduction to 3-D Geometry

Question

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

Moderate

A

$\frac{3}{2}$
B

$\frac{9}{2}$
C

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

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

Solution

$A B = \sqrt{2}, A C = \sqrt{20}, B = (3, 2, 0) and C = (0, 1, 4) N o w B C = \sqrt{26} ∴ l e n g t h o f t h e m e d i a n t h r o u g h A = \frac{1}{2} \sqrt{2 b^{2} + 2 c^{2} - a^{2}} = \frac{3}{\sqrt{2}}$

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