Show that A \left(\right. 1 , 1 , 2 \left.\right) , B \left(\right. 2 , 1 , 3 \left.\right) and C \left(\right. 1 , 3 , 5 \left.\right) are not collinear.

Engineering

Mathematics

Line of Greatest Slope

Question

Show that

A (1, 1, 2), B (2, 1, 3)

and

C (1, 3, 5)

are not collinear.

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A (1, 1, 2), B (2, 1, 3) a n d C (1, 3, 5)

D i r e c t i o n r a t i o o f \vec{A B}, = 2, 0, 1

D i r e c t i o n r a t i o o f \vec{B C}, = 1, 2, 2

T h e n A r e a o f Δ A B C = 0 t h e n i t i s c o l l i n e a r o t h e r w i s e i t i s n o t

\sqrt{{\sum (c_{2} b_{1} - b_{2} c_{1})}^{2}}

{\sqrt{{(0 - 2)}^{2} + (- 1 - 4)}}^{2} + {(4 + 0)}^{2}

\sqrt{4 + 25 + 16}, = \sqrt{45 \neq 0}

i t i s n o t e q u a l t o z e r o s o, i t i s n o n c o l l i n e a r

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