Unit vectors

1. Sep 7, 2008

xCanx

I am totally lost on this problem and I don't know where to begin.

If a and b are unit vectors that make an angle of 60 degrees with each other, calculate

l 3a - 5b l

the and and b have a carat of top of them

Can someone help me get started?

2. Sep 7, 2008

Staff: Mentor

Let a(hat) be x(hat), and draw b(hat) 60 degrees up counterclockwise towards y(hat). Express the above equation in rectangular coordinates, and do the vector subtraction. Then find the magnitude of the resultant vector. Does that help?

3. Sep 7, 2008

xCanx

I'm sorry I don't understand. It's only my third day of calculus class.

I don't understand what I am calculating?

4. Sep 7, 2008

Staff: Mentor

If I understand what you wrote, you are asked to ratio each vector by some scalar value (3 or 5), subtract the two vectors, then take the scalar magnitude of the resulting vector (that's generally what the "| |" symbol is use for with vectors.

Vectors can be expressed in either polar or rectangular form. Your textbook will discuss these forms, and how to convert back and forth between them. Since you are given information about the two vectors in this question initially in polar form (b is 60 degrees rotated from a), you will want to convert them into rectangular form to make them easier to subtract. You generally want vectors in rectangular form to do addition and subtraction.

So look at your book's explanation of rectangular and polar forms for expressing vectors, and the explanation of addition and subtraction of vectors in rectangular coordinates. Then look at how the book shows you to get the magnitude and direction of a vector (basically back to polar coordinates) for a vector that you have in rectangular coordinates.

That should get you going. Post your math as you work your way through the problem.

5. Sep 7, 2008

HallsofIvy

Staff Emeritus
$$|3a- 5b|= \sqrt{(3a-5b)\cdot(3a- 5b)}$$
and $$(3a- 5b)\cdot(3a- 5b)= 9a\cdot a- 30a\cdot b+ 25 b\cdot b$$

You are told that a and b are unit vectors and that they make an angle of 60 degrees (cos(60)= 1/2) so you should be able to find $a\cdot a$, $b\cdot b$, and $a \cdot b$ easily.