Finding the Coplanar Value of n for Given Vectors

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Homework Help Overview

The problem involves determining the value of n for which three given vectors are coplanar. The vectors in question are expressed in terms of their components along the i, j, and k axes.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the condition for coplanarity using the scalar triple product and explore the implications of their calculations. There are attempts to derive the value of n through vector cross products and dot products.

Discussion Status

Some participants have provided calculations and proposed values for n, while others have questioned the accuracy of these calculations. There is an acknowledgment of differing results, and some guidance has been offered regarding the coplanarity condition.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information available for discussion. There is a focus on ensuring the correctness of vector component calculations.

jarman007
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Homework Statement



The value of n so that vectors 2i + 3j - 2k , 5i + nj + k and -i + 2 j + 3k may be coplanar?

a)18 b)28 c)9 d)36


2. The attempt at a solution

I was not able to think of any step

so please help
 
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Hi jarman007, welcome to PF.
The vectors A, B and C are coplanar if A.(BXC) = 0
 
thanks and please check my solution

BxC = 10k -15j + nk + 3ni + j +2i = (3n+2)i -14j + (10+n)k


A.(BxC)=6n+4-42-20-2n=0

therefore n = 58/4
 
BxC = 10k -15j + nk + 3ni + j +2i = (3n+2)i -14j + (10+n)k
This calculation is wrong.
Check i and j coefficients. My answer is 18.
 
thanks

got the answer
 

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