# Further maths vector question

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I don't understand the first line of working. Why does the vector equation of AB have the same direction vector (5,4,3) as the two lines, when AB should technically be perpendicular to those lines and have a different direction vector? What am I missing here?

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I don't understand the first line of working. Why does the vector equation of AB have the same direction vector (5,4,3) as the two lines, when AB should technically be perpendicular to those lines and have a different direction vector? What am I missing here?

**alulaaustralis**)I don't understand the first line of working. Why does the vector equation of AB have the same direction vector (5,4,3) as the two lines, when AB should technically be perpendicular to those lines and have a different direction vector? What am I missing here?

What you say about AB being perpendicular to the lines is of course true, and this is what they do in the next stage (taking the scalar product of the vector from A to B with the direction vector of the lines) to work out the particular value of t that makes this work.

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Note that they aren't giving a vector equation for the line AB, they are giving the particular vector that takes you from A to B. The t in this expression is not a variable t that can take any value, it is one particular value that gives you the vector from A to B.

What you say about AB being perpendicular to the lines is of course true, and this is what they do in the next stage (taking the scalar product of the vector from A to B with the direction vector of the lines) to work out the particular value of t that makes this work.

**Pangol**)Note that they aren't giving a vector equation for the line AB, they are giving the particular vector that takes you from A to B. The t in this expression is not a variable t that can take any value, it is one particular value that gives you the vector from A to B.

What you say about AB being perpendicular to the lines is of course true, and this is what they do in the next stage (taking the scalar product of the vector from A to B with the direction vector of the lines) to work out the particular value of t that makes this work.

Thank you so much!

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**alulaaustralis**)

I don't understand the first line of working. Why does the vector equation of AB have the same direction vector (5,4,3) as the two lines, when AB should technically be perpendicular to those lines and have a different direction vector? What am I missing here?

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I see, so they have simply taken A away from B hence the t meaning μ - λ ?

Thank you so much!

**alulaaustralis**)I see, so they have simply taken A away from B hence the t meaning μ - λ ?

Thank you so much!

*particular*values of λ and μ that get you to A and B. So when they then say that t = μ - λ, that is one particular value of t that gives you the vector from A to B, which they then go on to determine.

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