Write 3 Scalar Eqns + System of 3 Linear Eqns for r,s,t

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Homework Help Overview

The discussion revolves around converting a vector equation into three scalar equations and a system of three linear equations involving the parameters r, s, and t.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to balance coefficients of the vector components (i, j, k) to form separate equations. Questions arise about how to express these relationships and whether the equations are already balanced.

Discussion Status

There is an ongoing exploration of how to derive the scalar equations from the vector equation. Some participants suggest that the equations are already balanced, while others seek clarification on how to explicitly form the equations from the given relationships.

Contextual Notes

Participants are working under the constraints of needing to express a vector equation in terms of scalar equations, focusing on the parameters r, s, and t without additional information on specific methods or solutions.

ronho1234
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-3i-j+5k = t (root34/102 (11i-13j+4k))-s(-j-k)+r(2i+2j+k)

how do i write this eqn as 3 scalar equations and a system of three linear eqns for the three parameters r,s, and t.

PLEASE HELP...
 
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hi ronho1234! :smile:
ronho1234 said:
how do i write this eqn as 3 scalar equations and a system of three linear eqns for the three parameters r,s, and t.

all the coefficients of i have to balance, also j and k …

those are your three equations :wink:
 
does that mean i get three separate equations each with the three variables... but how do i balance them like you said?...
 
ronho1234 said:
does that mean i get three separate equations each with the three variables

yes! :smile:

(and they're already balanced … write it out and see :wink:)
 
tiny-tim said:
yes! :smile:

(and they're already balanced … write it out and see :wink:)

Hey tiny-tim, what do you mean by it is already balanced. How do i form 3 equations using that relationship? Do I just make i, j, k the subject?
 
hey kihakuu! :smile:

this is a vector equation, so all three component equations have to be true :wink:

for example, the "i" components equation for -3i-j+5k = t (root34/102 (11i-13j+4k))-s(-j-k)+r(2i+2j+k)

would be -3i = t (root34/102 (11i)+r(2i) :wink:
 

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