How to solve k_b bar(b)−k_a bar(a)+1/t * k_a bar(a)-1/t(bar(c)-bar(a)_1)=bar(a)_1−bar(b)_1

Emmanuel Pace

Emmanuel Pace

Answered question

2022-07-16

How to solve k b b ¯ k a a ¯ + 1 t k a a ¯ 1 t ( c ¯ a ¯ 1 ) = a ¯ 1 b ¯ 1

Answer & Explanation

salumeqi

salumeqi

Beginner2022-07-17Added 15 answers

Here is a way to calculate t when a is not parallel to b
Define d c a 1 and e a 1 b 1 and f a × b
multiply through by t to get ..
(1) t k b b + ( 1 t ) k a a = d + t e
taking the dot product with f we have ...
0 = d f + t ( e f )
So that
t = d f e f
note that no solution exists if ( d f ) = 0 or ( e f ) = 0
If f = 0 then solutions only exist if ( d × b ) × ( e × b ) = 0 and ( d × a ) × ( e × a ) = 0

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