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# Equality of vectors

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1. In M1, i am very confused with how to make vectors equal. For example in this question; Given that a = 2i + j and b=i+3j find x if a + xb is parallel to the vector i. I know that I have to form some sort of simultaneous equation and the answer is -1/3, but I can't work out how to get there? Thanks!
2. (Original post by mayjb)
In M1, i am very confused with how to make vectors equal. For example in this question; Given that a = 2i + j and b=i+3j find x if a + xb is parallel to the vector i. I know that I have to form some sort of simultaneous equation and the answer is -1/3, but I can't work out how to get there? Thanks!

Do what RDKGames said
3. (Original post by mayjb)
In M1, i am very confused with how to make vectors equal. For example in this question; Given that a = 2i + j and b=i+3j find x if a + xb is parallel to the vector i. I know that I have to form some sort of simultaneous equation and the answer is -1/3, but I can't work out how to get there? Thanks!
For the expression to be parallel to i, the j component must be 0.
4. (Original post by RDKGames)
For the expression to be parallel to i, the i component must be 0.
I understand that, but I don't know what you do if it gets more complicated and is equal to say -i-3j?? I just don't understand the method you follow to get to the answer.
5. (Original post by mayjb)
I understand that, but I don't know what you do if it gets more complicated and is equal to say -i-3j?? I just don't understand the method you follow to get to the answer.
Then yes, simultaneous equations. You would need 2 scalars for both vectors in order to reach any point/vector in the plane from two vectors which aren't parallel to each other, so that's where the two variables come from.
6. (Original post by mayjb)
I understand that, but I don't know what you do if it gets more complicated and is equal to say -i-3j?? I just don't understand the method you follow to get to the answer.
Do you understand that if vectors and are parallel then (scalar constant k), if so it's not too hard to see that a vector parallel to the x axis the vector must be of the form .

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