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If Vector a = Vector AB and vector b=vector BC are two adjacent side of a regular hexagon ABCDEF. Find

the vector CD, vector DE , vector EF , vector FA, vector AE , vector CE in terms of vector a &b.

Asked by Kusum and Sanjeet 13th May 2016, 4:36 PM
Answered by Expert
Answer:
C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
G i v e n space t h a t space A B C D E F space i s space a space r e g u l a r space h e x a g o n comma space w i t h space stack A B with rightwards harpoon with barb upwards on top equals a with rightwards harpoon with barb upwards on top space a n d space stack B C with rightwards harpoon with barb upwards on top space equals b with rightwards harpoon with barb upwards on top space
S i n c e space i t space i s space a space r e g u l a r space h e x a g o n comma space A D space i s space p a r a l l e l space t o space B C space s u c h space t h a t space A D equals 2 B C
rightwards double arrow stack A D with rightwards arrow on top space equals 2 stack B C with rightwards arrow on top
rightwards double arrow stack A D with rightwards arrow on top space equals 2 b with rightwards arrow on top

I n space t r i a n g l e space increment A B C comma space w e space h a v e comma
stack A B with rightwards arrow on top plus stack B C with rightwards arrow on top equals stack A C with rightwards arrow on top
rightwards double arrow a with rightwards arrow on top plus b with rightwards arrow on top space equals stack A C with rightwards arrow on top

I n space t r i a n g l e space increment A C D comma space w e space h a v e comma
stack A C with rightwards arrow on top plus stack C D with rightwards arrow on top equals stack A D with rightwards arrow on top
rightwards double arrow stack C D with rightwards arrow on top space equals stack A D with rightwards arrow on top space minus stack A C with rightwards arrow on top
rightwards double arrow stack C D with rightwards arrow on top space equals 2 b with rightwards arrow on top space minus open parentheses a with rightwards arrow on top plus b with rightwards arrow on top space close parentheses
rightwards double arrow stack C D with rightwards arrow on top space equals 2 b with rightwards arrow on top space minus a with rightwards arrow on top minus b with rightwards arrow on top
rightwards double arrow stack C D with rightwards arrow on top space equals b with rightwards arrow on top space minus a with rightwards arrow on top

F r o m space t h e space f i g u r e comma space i t space i s space c l e a r space t h a t comma
stack D E with rightwards arrow on top equals negative a with rightwards arrow on top
stack E F with rightwards arrow on top equals negative b with rightwards arrow on top
stack F A with rightwards arrow on top equals negative stack C D with rightwards arrow on top space equals negative open parentheses b with rightwards arrow on top space minus a with rightwards arrow on top close parentheses equals a with rightwards arrow on top minus b with rightwards arrow on top
Answered by Expert 14th May 2016, 9:14 AM
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