# vector

1. ### Vector problems

Hi, I just made this account. I need help to check if I did my this right. 1. Determine a vector a of opposite direction from vector b=-2i+j. The length of a is 3√5. 2. Draw in the coordinate system a vector a=3i-j Thank you in advance
2. ### sin(x) as a vector

Hi! I could do with some help on an assignment for my calculus class! This is the info given at the beginning of the assignment: Fourier series can be seen as a generalisation of the idea of the scalar product. Consider on the one hand the ordinary vectors v1 = (1, 1) and v2 = (1,°1), and on...

I would like to know whether I am correct in my thinking below. You can add two vectors using basic arithmetic only when either two cases occur: (1) the vectors are parallel to each other (2) the vectors direction are opposite of each other (in which case, you could multiply one of the...
4. ### Find the magnitude and bearing of the vector v=<5,-7> to the nearest whole vaule

How do i find the answer?
5. ### What is the direction angle of the resultant <34,-21>

How do I solve this?
6. ### Cross product properties

Hi, Could someone explain for me how the first line led to the second line in the image below? I'm a familiar with cross product, but this case scenario confuses me. - otownsend
7. ### Scalar projection question

Hi, I hope someone can help me with the following question: Some step-by-step guidance would be helpful since I'm not sure where to start!
8. ### Vector and scalar projection help

Hi, I'm looking for help for the following question: I was able to figure out 12a, but I can't seem to figure out the rest of the subquestion for 12. Here are some questions I have: For (12b) - when relocating vector b, does the new spot have to be tail-to-tail with vector c in order for...
9. ### Multiplication of vectors question

Hi, I'm hoping someone can point out what I did wrong for the following question. My answers don't match the textbook's, so I'm assuming something is wrong. Here is the question: Here is my solution: I didn't end up finishing the calculation for finding the direction since 1.24 was...
10. ### General solution in vector form

Hi, I'm currently trying to understand the general solution to a system of linear equations in vector form. Let's say that when the system is in row reduced matrix form, there is a column will all zeros. According to the image that I took from a textbook, a zero column would suggest the...
11. ### Graphical analysis of linear systems

Hi, I'm in the midst of solving the question below: I am pretty certain that b is a solution - based on the parallelogram rule (it seems to be a linear combination of c1v1 + c2v2 + 0v3). In terms of the type of solution... I'm not really sure. One thing that I do notice, is that one of...

Decide an equation in general form for a plane that is parallel to the vectors u and v and goes thru the point P=(1, 0, 3). Vectors: u=(1, -2, 0) v=(3, -5, 1) --- If the terminology is incorrect it is because I have tried to translate it from Swedish: "Ange, på normalform, en ekvation för det...
13. ### Pilot and wind velocity vector help

A pilot needs to fly 35 degrees east of north. He's flying at a speed of 105 miles per hour at fixed altitude with no wind. When he reaches a point, he encounters wind with a velocity of 15 miles per hour in the direction 10 degrees east of north. Express the velocity of the wind W as a vector...
14. ### Divergence of vector field

If we consider the limit case of eg. shrinking a coin, surely at Volume=0 then the diameter of the coin will be 0? Since a coin of volume zero cannot have a diameter (to have a diameter it needs to have a volume of more than zero)? This random question arose when studying the divergence of...
15. ### vector calculus- application of Stoke's theorem

Q1. Use Stoke's theorem to evaluate int(x^2*exp(5*z) dx +x*cos y dy+3*y dz) around a closed curve C where C is defined by the parametric equation x=0, y= 2(1+cos t), z=2(1+sin t), 0<=t<=2 Pi. Q2. Let S denote the surface of a cylindrical solid bounded by x^2+y^2 =...
16. ### vector product and vector sum

what is the vector sum of (2,10,-50) and (30,-4,0) and also explain the definition of vector sum and vector product.vector
17. ### Need Help With Change of Variables from Cartesian to Spherical Coordinates

Hello there! Cutting straight to the chase, I need help with the derivation best described in this video here @ 7:48: https://youtu.be/AjDSLq-Pzcs?t=7m48s By this point in the video, Adam Beatty has already established: x=r*cos(Φ)*sin(θ) , y=r*sin(Φ)*sin(θ) , z=r*cos(θ) It also makes sense to...
18. ### Unit tangent vector vs principal normal vector difference

http://mathwiki.ucdavis.edu/Core/Ca.../The_Unit_Tangent_and_the_Unit_Normal_Vectors In the link, I cant understand that why the Principal Unit Normal Vector is defined by N(t) = T'(t) / | T'(t) | ,can someone explain.... Since tangent vector is normal to principal normal vector, why the N(t)...
19. ### normal vector in surface integral of vector field

when the normal vector n is oriented upward , why the dz/dx and dz/dy is negative ? shouldnt the k = positive , while the dz/dx and dz/dy is also positive?
20. ### vector field

sketch the F(x,y)=yi + j refer to part c , i dont understand the direction of arrow drawn , for (x,y) = (1, 0) , F(x,y) = <0,1> , why the arfow shouldnt point from (1, 0) to <0,1> ? (red arrow) i dont undertstand .....