Finding the Coplanar Value of n for Given Vectors

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To determine the value of n for the vectors 2i + 3j - 2k, 5i + nj + k, and -i + 2j + 3k to be coplanar, the condition A.(BXC) = 0 must be satisfied. The cross product BXC was calculated incorrectly, leading to an erroneous conclusion. After correcting the coefficients for i and j, the correct value of n was found to be 18. This indicates that the vectors are coplanar when n equals 18. The final answer confirms the solution as accurate.
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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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