Math Help

Archive for July, 2008

Question: Help With Math Vectors?

Hello all

This question is about vectors. I have two vectors:-

F1 = 7, its direction is vertical acting upwards.
F2 = 11, its direction is horizontal acting to the right.

Find the angle the resulant vector creates.

If i draw these vectors on an xy plane, i get an arrow of length 7 pointing upwards and a second arrow pointing sideways pointing to the right.

I could draw these vectors in two ways, i could join the head of the first vector to the tail of the second vector or draw the two vectors in standard postion i.e from 0,0.

So even though the resulant vector is the same the angle the resultant vector creates will be different depending on which way it is drawn i.e either 57.5 degrees or 23.5 degrees,
which is correct?
what is the correct method for drawing vectors? ie, joining the vectors head to tail or from standard position.

Can anyone help?

Thank you.

Answer: I think you are missing the most important part of vectors. Vectors decompose a function into functions that contain 2 or more components. in other words, there is no vector of 7 or 11
for F1
this vector is going straight up, so it has no horizontal displacement. This is not that same as saying it has no horizontal component. Its horizontal component is 0.
so
F1 = <0,7> and likewise
F2 = <11,0>
These are both component vectors, you add them together to get V
V = <0,7> + <11,0> = <11,7>
this vector has a length or magitude of the root of the sum of their squares
||V|| = rt(121+49) = rt(170)
its unit vector is the vector divided by its magnitude
1/rt(170)<11,7>
It has an angle wrt to the x axis of
tan(theta) = 7/11
arctan(7/11) = theta = ~32.47deg

joining vectors is addition. You join head to tail. It does not matter which head is joined to which tail. If you do both, you will get a paralellagram, in your case the paralellagram is a rectangle. if you join F1 to F2, and then join F2 to F1, both heads should meet at the same point, in this case the point (11,7) assuming you started at the origin.

If you learned this stuff in engineering, they use the i, j, k notation instead of the notation used in math. the problem with the engineering method is that its easy to forget that a missing component is actualy a component equal to 0.

Vectors – The Dot Product

This section of Math Help online discusses Integration by parts, a popular method of Integration whenever possible. Integration by parts Integration method is based on the math formula: 

d (uv) = u dx + v du 

This math formula corresponds to the Integration formula: 

 

By re-arranging the above Integration math formula, we have our Integration by parts formula: 

 

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Integration by parts involve recognizing the function u and dv and manipulating the functions into the form above. 

If a definite integral is involved, then: 

 

Click here to go to an example of how to solve an Integration problem using Integration by parts.

Question: math question, multiplication of rational expressions?

X+ 13 X ( X-3)
______ . _______
3
X (3-X) 5

Can anyone help me out with this problem? it’s the multiplication of ration expressions which i tried to write as best as i could (notice the bottom left variable has an exponent and on the top, X + 13 is separate from the other). * Please and ty*

PS. don’t give me an answer just help out with it if you can
ok so i begin by mult. the x’s on both sides?

Answer: Sorry, but what you wrote doesn’t display right on my computer, so I can’t see what the problem is. Still, I’ll try…

Rational expressions are basically fractions. When you multiply fractions, you multiply the numerators together and the denominators together. That’s essentially the idea here.

Math Help Exponents 3: Multiplication