# vectors

1. ### Planes and Lines I

There are four problems I need to know how to solve before an exam and I just can't. I was hoping that I could get some help here! Question 1: A point is mirrored in the line 4x + 3y = 0. The position of the mirrored point is (-5, 3). What is the position of the original point?
2. ### Line Integral Help

Can anyone explain to me why the image is true?
3. ### Given a vector starting point P = (-2,3) and ending at the point Q = (5,-1)

Given a vector starting point P = (-2,3) and ending at the point Q = (5,-1), find the x and y components. How do i solve this
4. ### Find the coordinates of the point Q given these conditions...

Given X = <-1, 2>, Y = <5, 5>, Z = <2, -1>. Q is on the segment YZ where the length of the segment YQ is double the length of the segment QZ. I'm trying to do this without calculating any lengths. Looks like something to do with a linear combination of vectors.
5. ### Distance between lines in R^3

Hi, I'm trying to determine the distance between the following lines: To solve this question, I'll be using the following distance formula: I know that the vector 'm' would be (1,1,3), but in terms of vector 'QP' I'm not sure how to determine this. Can someone help? - otownsend
6. ### Identifying points from lines

Hi, I hope someone can help. I know that the direction vector for line 1 is (2,1,-1) and for line 2 is (3,2,-3). Not sure where to go from here. - otownsend
7. ### Vector equations in R^3

Hi, I'm trying to understand the question below: The solution is: Can someone explain how the parametric vector equation for 'z' was created? Also, how do you know what a "suitable restriction" is ? - otownsend
8. ### Vectors - determine "k"

Hi, Can someone help guide me towards solving this question? This is what I've done so far: - otownsend
9. ### Velocity and vectors

Hi, I'm looking for help with the following question: It appears that I got question (a) correct. However, my solution for question (b) is apparently wrong - the correct solution is apparently 100s. Here is my work: Can someone help identify where I went wrong in my solution? - otownsend
10. ### Dimension of subspaces

Hi, Just hoping that someone can help me better understand the dimension of a subspaces. To start, I will show this paragraph: So there's a matrix that has 3 columns and 4 rows. I don't understand, fundamentally speaking, why the matrix would be a 2-dimensional subspace of R^4. I understand...
11. ### Projection Thereom- When Proja Is equal for 2 Vectors, Prove the Dot Product is equal

Hi There I'm really struggling with these question: Projau = Projav is true for some vectors a, u and w. Show: u · v = v · a Show: counter example to show that u isnt equal to v I seem to have these looooooooong roundabout routes that arent making sense for the first, and for the second i...
12. ### Vector projection onto a plane

Find the value(s) for k such that the projection of the vector v ​= (3, k, 7) onto the xy-plane has a magnitude of 6. I'm very bad with projections and I can't find anything that helps.
13. ### Vectors in 3Space

I need help on a problem for my Calc 3 class. A surveyor is standing at a point A 300 feet away from a tall building. Let i, j, k be the direction of east, north, and up respectively. She observes that a vector in the direction of A is 3i + 4j + 15k, where C is the highest point of the...
14. ### Finding S and S^-1 in Eigen vectors / values

Hey Guys, I am a bit stuck on how to get S and S^-1. I understand how to get landa but I don't know how to get the other two matrices as shown.
15. ### Eigenvalues and Vectors

Hi, Our lecturer covered this very quickly and I can't find anything in any of my texts to help. I understand that: We need to put it in form -(A - L (landa) I ) v and put it equal to zero; A - L I must be singular; He then said just to form A - L I and to do that subtracted L from the...
16. ### Triangle Problem using Vectors

Hi I have a question regarding vectors and how to solve problems given a set of points forming a triangle. "For triangle ABC, with vertices A=(1,2,2), B=(0,-2,1) and C=(1,5,-1) find: (a) the length of side AB - I have done this; (b) the equation of the line that passes through A & B - we...