MIchael Driesen Mrs. Rozell Math 10H 17 December 2011 Vectors Math is everywhere. No matter which way you look at it, it’s there. It is especially present in science. Most people don’t notice it, they have to look closer to find out what it is really made of. A component in math that is very prominent in science is the vector. What is a vector? A vector is a geometric object that has both a magnitude and a direction. A good example of a vector is wind. 30 MPH north. It has both magnitude,(in this case speed) and direction. Vectors have specific properties that make them very useful in real life applications. Through the use of these special objects, many advancements in the fields of math and science are available. Representations …show more content…
The equation for the cross product is: . It can also be written as: The easiest way of finding the cross product is by setting the coordinates up in a 3x3 matrix. A matrix is a way of organizing data. Using i, j, and k as place holders and using the same two vectors from before, the matrix would look like this: Now, in order to get the new vector, the determinant has to be found. The work for the determinant is below: The final vector is a vector that is orthogonal to the other two. This is a good representation of what it would look like: The cross product is necessary to find the amount of torque or work needed or used. Other Vectors Null Vector: The null vector is a vector that has the length (magnitude) of 0. It is written as (0,0,0) and if c is a null vector and a is a normal one, c+a=a. Unit Vector: This vector is more about direction than magnitude. The unit vector has a magnitude of one, always. Turning a vector into its unit vector is easy. Just divide the vector by its magnitude. This is called the normalization of a vector. Adding Vectors Adding vectors is very easy. All that is needed is a knowledge of trigonometry. Specifically, the law of cosines and the law of sines. To add two vectors, simply stick them head to tail, and
I found the secret formula, it was (w+L)-2 but w/l had to be reduced so it
A(-2, 2) becomes A'(5, 1) , B(-2, 4) becomes B'(5, 3) , C(2, 4) becomes C'(9, 3) , D(2, 2) becomes D'(9, 1)
To determine the location of point (3,2) when rotated using matrix A, matrix multiplication must be applied. The work below shows
Running with this information can now write out the equation AB2 + BC2 = AC2. One important thing is that we must note that AB is equal to “X” and the line segment of BC is equal to that of 2x+4, and that AC will be equal to that of 2x+6. So we will now input this information to create (x)2 + (2x + 4)2 = (2x + 6)2 and begin factoring each term into two sections. These two sections will be as x*x + (2x + 4)(2x + 4) = (2x + 6)(2x + 6). x times x is x2. An important tool to use now would be the FOIL method, so we will take (2x + 4)(2x + 4) and create 4x2 + 16x + 16. Right off the bat we notice that we have like terms. So we will add x2 to 4x2 to get 5x2. This will create 5x2 + 16x + 16 = 4x2 + 24x+ 36. Now we will use the subtraction property to get 5x2 – 4x2 + 16x – 24x + 16 – 36 = 0, however we still have like terms, so because 5x2 is a like term with -4x2 we will add them together to get x2. We will also combine 16x and –24x and also 16 and –36 which are also like terms and create –8x and –20, our equation should now look like x2 – 8x -- 20 = 0.We will now factor the equation from left to right, first factoring x2 which has 1 coefficient so the fact will be 1 and -1. The other term will be 20 which have no coefficient so we will do 5x4 and then 4 still can be divided so 2x2. This will create 20=225.
43. A stone is shown at rest on the ground. A. the vector shows the weight of the stone. complete the vector diagram showing another vector that results in zero net force on the stone. B. what is the conventional name of the vector you have drawn?
Step Five: If we substitute this with the information we came up with in step three then we have a2+b2=c2.
Math and Science are two subjects which most students at any level approach with trepidation and intense dislike, however, both subjects are integral to cognitive thinking. Not only will these subjects provide skills that will help students think more clearly, but students will be academically successful throughout their school career, enjoy wider career choices and
A question that sometimes is mentioned is how can algebra make our lives easier? Some people assume that our need for math is basic. This is saying that we should be fine as long as we can add, subtract, multiply, and divide. What these people do not realize is that algebra is used in our lives more than they think. For students, determining your grade-point-average (GPA) and understanding what is your class grade takes a bit of algebra to understand. For example, if a high school student wants to determine what their GPA for admission to a university, they have to know what numbers represent the letter grades. Traditionally,
In my WIKA for week 5 on algebra (Appendix N) I explain that algebra is used as a means of representing data or something that simplifies an expression. I go on to explain the ways in which algebra has been used in physics and mathematics and is the backbone of each and every formula in these and other scientific disciplines and even give an example of how algebra can be used to simplify very abstract problems.
My leader Galileo influenced modern day science by using experiences of mathematics he learned. Mathematical corresponds with science in different ways. For example in Earth science, we have to use equations to solve something, such as density. Conversion between units, measurements and much more. It is up to the person to open doors of how science connects to almost
In my schooling, I studied subjects that include science along with mathematics which helped me to develop awareness in the above courses.
rotates counterclockwise. What are the sizes of the x and y components of the vector for
It is often said that math and science are two subjects that go hand in hand. Much of the work that scientists do, is conduct experiments to produce data. In most cases, the data involves numbers. Whether it involves weight, speed, time, temperature, etc., that data is mostly quantifiable. In order to solve problems, scientists, as well as students striving to be scientists must use the basic forms of algebra to accurately solve their calculations. Being a chemistry major, I have found that as a student progresses to higher level chemistry, the courses become more math intensive, this being a challenge for those who did not succeed in the following college algebra topics.
Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to be regarded increasingly as the science of relations, or as the science that draws necessary conclusions. This latter view encompasses mathematical or symbolic logic, the science of using symbols to provide an exact theory of logical deduction and inference based on
If the load is applied at the mid- length a=b=L/2 then mid span deflection is: