First slide

Introduction to 3-D Geometry

Question

$A (0, 2, 3), B (2, - 1, 5), C (3, 0, - 3)$ are vertices of $Δ A B C .$ If a,b,c are HG, GS, SH then their increasing order is (H,G, S are orthocentre, centroid and circumcentre)

Moderate

A

a,b,c
B

c,b,a
C

b,a,c
D

b,c,a

Solution

$A B^{2} + C A^{2} = B C^{2}; ∠ A = 90$
triangle is right angle triangle
orthocentre=H=(0,2,3)
G=centroid=(0+2+3/3,2-1+0/3,3+5-3/3)
S=circumcentre =mid point of hypotenuse

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