## Vector product

1. The problem statement, all variables and given/known data

Consider the two vectors L= i +2j+3K
K=4i+5j+6k
Find scalar 'a' such that:
L - aK is perpndicular to L.

2. Relevant equations

if two vectors are perpenicular dot product=0

3. The attempt at a solution

(i+2j+3k).{(1-4a)i+(2-5a)j+(3-6a)k}=0
I get three values of a here. but none satisfies th whole equations at the same time. Please help me
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 I don't understand what you mean by the last line. Can you show us how you calculated the dot product? Surely it yields a linear equation in a? How can it possibly result in 3 values for a? There is only one equation, how can you not be able to find one a that satisfies the whole equation at the same time? You probably made a mistake with the dot product: $$(a \hat{i} + b\hat{j} + c\hat{k} ) \cdot ( d\hat{i} + e\hat{j} + f\hat{k}) = ad + be + cf$$

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 Quote by xphloem 3. The attempt at a solution (i+2j+3k).{(1-4a)i+(2-5a)j+(3-6a)k}=0 I get three values of a here. but none satisfies th whole equations at the same time. Please help me
Complete the dot product you wrote, using Nick89's formula if you didn't know it already. You'll get a linear equation in a.

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