Answered: Write down the line equation a) given a…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Additional Topics In Trigonometry

Section: Chapter Questions

Problem 33CT

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Question

Write down the line equation

a) given a point Q and a vector v.

b) given two points R and Q.

Expert Solution

Step 1

$S i n c e, o u r a i m i s t o f i n d t h e e q u a t i o n o f a l i n e t h a t i s : - (a) p a s \sin g t h r o u g h a g i v e n p o i n t Q a n d a v e c t o r v . (b) p a \sin g t h r o u g h t w o g i v e n p o i n t s R a n d Q .$

Step 2

$(a) E q u a t i o n o f a l i n e t h a t i s p a s s i n g t h r o u g h a g i v e n p o i n t Q a n d a v e c t o r v . L e t \overset{⇀}{v} b e t h e p o s i t i o n v e c t o r o f t h e g i v e n p o i n t Q w i t h r e s p e c t t o t h e o r i g i n O o f t h e r e c t a n g u l a r c o o r d i n a t e s y s t e m . L e t l b e t h e l i n e w h i c h p a s s e s t h r o u g h t h e p o i n t Q . L e t \overset{⇀}{u} b e t h e p o s i t i o n v e c t o r o f a n y a r b i t r a r y p o i n t R o n t h e l i n e, t h e n : - \overset{⇀}{QR} = \overset{⇀}{OR} - \overset{⇀}{OQ}$

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