Question

Good afternoon! Can someone explain the Vectors in the plane.

Answer 1

vectors in one plane... that would mean in two dimensions?
Just go through the first section here.
http://www.physicsclassroom.com/class/vectors/

Answer 2

There's two basic operation for vectors right? The scalar multiplication and vector addition. What is the difference between of two of them?

Answer 3

oh, I thought you were looking for general information on vectors. You want to know the difference between the scalar or dot product and the vector or cross product?

Answer 4

Yes all about the vectors.

Answer 5

all about vectors is too much to teach in one day, but I could try to find websites for you to learn from. what math class are you in so I can know what exactly you want me to teach?

Answer 6

No. I just need to have someone who is willing to share some ideas about vectors then I will share what I've know in vectors. If its alright to you?

Answer 7

ok. vectors represent moving from one point to another. They have a magnitude and direction, but are usually represented by an x-coordinate and a y-coordinate in 2 dimensions.

Answer 8

vectors add by placing the vectors tip-to-tail and seeing where it goes or by breaking down the vectors into their x and y components and adding all the components.

Answer 9

the dot product or scalar product is the vector operation where you multiply one vector A by the component of another vector B that is parallel to it. The product is a scalar. It is given by AB sin (the angle between the two vectors)

Answer 10

the scalar product of two vectors A and B with the components \[(X _{a}, Y_{a}) and (X_{b}, Y_{b})\] is \[X_{a} \times X_{b} + Y_{a} \times Y_{b}\]

Answer 11

the cross product or vector product of two vectors is the vector operation where you multiply one vector A with the component of vector B that is perpendicular to vector A. The resultant vector is perpendicular to both vector A and vector B, in the direction given by the right hand rule. (ask your math teacher, I dont think I can explain this one here.)

Answer 12

For example, I am asked to show that if A is any vector and c is any scalar 0(A)=0 and c(0)=0. How will I compute the magnitude of vector cA?

Answer 13

the magnitude of cA will be c times the magnitude of vector A.
do you need to know how to find the magnitude of a vector?

Answer 14

Yes. I just remember the difference of two vectors. If the difference of vectors A and B, it is denoted by A-B, is the vector obtained by adding A to the negative of B or rather A-B = A+(-B). Am I right?

Answer 15

Yes, you are right.

Answer 16

In orthogonal vectors, two vectors A and B are said to be orthogonal or perpendicular if and only if A DOT B = 0.

Answer 17

yes, by definition of the dot product, if two vectors are perpendicular their dot product is zero.

Answer 18

\[A\cdot B = |A||B|\cos\theta\]
If orthogonal implies\[\cos\frac{\pi}{2}=0\]
Hence\[A\cdot B =0\]

Answer 19

Just saying, the identity\[A\cdot B = |A||B|\cos\theta\] is not the definition of dot product. If I recall, this can be traced back to the Cauchy-Schwarz theorem where\[(A\cdot B)^2 \leq |A|^2|B|^2\] Equality holds when \[A=B\]

Answer 20

Or you can use the law of cosine if you like.

Answer 21

Most of the time we use the law of cosine in our discussion.

Answer 22

It is indeed more straightforward.

Answer 23

A sneak peek in cross product.

A cross product between 2 vectors produce the third vector which is orthogonal to both the original 2 vectors.

Answer 24

Is that a theorem?

Answer 25

It is the definition

Answer 26

ok.Thanks