Physics help!!!?

please help me with these questions...


1).given 2 vectors A = 4.00i + 3.00j and B =5.00i - 2.00 j, a)find the magnitude of each vector; b)write an expression for the vector difference A - B using unit vectors; c)find the magnitude %26amp; direction of the vector difference A - B.





2) a)is the vector (i + j + k) a unit vector? justify your answer; b)can a unit vector have any components w/ magnitude greater than unity? can it have any negative components? in each case justify your answer; c) if A = a(3.0i + 4.0j), where a is a constant, determine the value of a that makes A a unit vector.








oh please.., help me with these 2 problems...


thank you in advance :-)

Physics help!!!?
1. a) magnitude=sqrt(a^2+b^2+c^2+...etc)


magnitude=sqrt(4^2+3^2)


=5


magn=sqrt(5^2+(-2)^2)


=sqrt(29) or 5.385





b) Just treat i and j as variables. A-B (just sub in the equations and evaluate). A-B=(4i+3j)-(5i-2j)


Difference= j-i





c) magnitude=sqrt(1^2+(-1)^2)


=sqrt2 or 1.4


Direction: Draw out the two vectors and use tan. Each vector has a magnitude of 1 since they are unit vectors.


Therefore tantheta=opposite/adjacent


tantheta=1/1


theta=45º.





2. a) I don't think it's a unit vector because unit vectors have a magnitude of 1. To determine the unit vector, you put the vector in coordinate form so vector=(1,1,1) and divide it by the magnitude (magn=sqrt(1^2+1^2+1^2)=sqrt3)


Therefore the unit vector in that direction is actually (1/sqrt3,1/sqrt3,1/sqrt3)





b) One condition of a unit vector is that is has a magnitude of 1. Anything greater is not a unit vector, it is a multiple of that unit vector in the given direction. I imagine a unit vector could have negative components if it is in a negative direction.





c) A=a(3i+4j) Remember unit vectors have a magnitude of 1. so set A=1 and convert (3i+4j) into a magnitude as shown above. Therefore magnitude=5. so then "a" equals 1/5 I imagine. The unit vector is (3/5,4/5) as shown above when I stated a unit vector is the coordinate form divided by the magnitude. So with that said, a=1/5 I think.

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