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# help with this M1 vectors question watch

1. Given that a= 2i + 5j and b= 3i - j, find

P if a+Pb is parallel to the vector i

Solution:

a+Pb= (2i+5j) + P(3i-j)=(2+3P)i + (5-P)j
Parallel to i, so 5-P=0, P=5.

I don't get the part about the vector being parallel to i. Why is the bracket made equal to 0? And why only that bracket and not the other one?

Thanks
2. (Original post by ms94uk)
So they ask for paralled vectors to i so surely both i components must be the same so you need you multiply b by some sort of constant to achieve it do you get it or still nothing?
No I don't get it as we rushed through vectors in class and our teacher didn't teach it well
3. Well, if it is parallel to i, surely the j component is 0. If it were not 0, it wouldn't be parallel to i
4. If you have two vectors, and you are trying to make a+ (X)b where (X) is a const. Calculate then that gives you : 2i+5j + (X) (3i-j) now collect same i and j terms so you get 2+ 3(X) i + 5-1(X)j if its parallel to i that means it must be flat since i is horizontal so surely j component must be zero but because our j component is 5-1(X) therefore 5-1(X)=0, (X)=5

Remember i is one unit to the left and j is one unit upwards so if vector is moving parallel to i that means is a flat line eg 14i it cant have j component because j component would make it move up or down and it must continue moving in a same straight line as x axis or i component

Get it now?
5. (Original post by ms94uk)
If you have two vectors, and you are trying to make a+ (X)b where (X) is a const. Calculate then that gives you : 2i+5j + (X) (3i-j) now collect same i and j terms so you get 2+ 3(X) i + 5-1(X)j if its parallel to i that means it must be flat since i is horizontal so surely j component must be zero but because our j component is 5-1(X) therefore 5-1(X)=0, (X)=5

Remember i is one unit to the left and j is one unit upwards so if vector is moving parallel to i that means is a flat line eg 14i it cant have j component because j component would make it move up or down and it must continue moving in a same straight line as x axis or i component

Get it now?
Thanks a lot I get it now

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