 # Vector Examples, Equations, and Practice Problems

Recent questions in Vectors Riley Barton 2023-03-29

## Find, correct to the nearest degree, the three angles of the triangle with the given verticesA(1, 0, -1), B(3, -2, 0), C(1, 3, 3) Audrey Hall 2023-03-25

## How to find the angle between the vector and $x-$axis? umatisi6ar 2023-03-11

## Define vector analysis? obklopit90r9 2023-02-25

## What is the terminal point of a vector? imbustatozyd6 2023-02-25

## How to find a unit vector with the same direction as 8i - j + 4k? Admiddevadxvi 2023-02-21

## Let $\stackrel{\to }{A}$ be vector parallel to line of intersection of planes ${P}_{1}$ and ${P}_{2}$ through origin. ${P}_{1}$ is parallel to the vectors $2\stackrel{^}{j}+3\stackrel{^}{k}$ and $4\stackrel{^}{j}-3\stackrel{^}{k}$ and ${P}_{2}$ is parallel to $\stackrel{^}{j}-\stackrel{^}{k}$ and $3\stackrel{^}{i}+3\stackrel{^}{j}$ then the angle between vector $\stackrel{\to }{A}$ and $2\stackrel{\to }{i}+\stackrel{\to }{j}-2\stackrel{^}{k}$ Jaelyn Mueller 2023-02-18

## How to find a unit vector normal to the surface ${x}^{3}+{y}^{3}+3xyz=3$ ay the point(1,2,-1)? FeelryclurN9g3z 2023-02-16

## How do I find the magnitude and direction angle of the vector $v=3i-4j$? Elaina Mullen 2023-02-09

## How to find a unit vector a) parallel to and b) normal to the graph of $f\left(x\right)=-\left({x}^{2}\right)+5$ at given point (3,9)? kariboucnp 2022-12-31

## can the vector components be negative erishita9od 2022-12-18

## Is momentum a scalar or vector? Maxwell Mccoy 2022-12-15

## A quantity which has both magnitude and direction is called ______. LahdiliOsJ 2022-11-27

## Which of the following are vectors and which are scalars: Distance, mass, time, weight, volume, density, speed, velocity, acceleration, force, temperature and energy? valahanyHcm 2022-11-26

## Which one of the following is a vector quantity? A)Distance B)Displacement C)Position D)Speed gheadarce 2022-11-24

## If I have ${\stackrel{\to }{w}}_{1}=\left(2,3\right)$ and ${\stackrel{\to }{w}}_{2}=\left(1,1\right)$, but they are relative to the basis $\stackrel{\to }{u}=\left(1,1\right),\stackrel{\to }{v}=\left(1,-1\right)$. How do I find the scalar product of ${w}_{1}$ and ${w}_{2}$?I know that $⟨{w}_{1},{w}_{2}⟩=2\cdot 1+3\cdot 1$ when the basis are orthogonal, but that is not the case here. Would I say that ${w}_{1}=2\cdot 1+3\cdot 1$ and ${w}_{2}=1\cdot 1+1\cdot -1$? If so, then how do I proceed from here? Salvador Whitehead 2022-11-24

## Find the directional derivative of $f={x}^{2}·y·{z}^{3}$ along the curve at the point P where u = 0My working:At u=0, x=1, y=1, z=-1 so let u = (1,1,-1).Know that ${D}_{u}f\left(x\right)=\nabla f\left(x\right)·u=\left(2x·y·{z}^{3},{x}^{2}·{z}^{3},3{x}^{2}·y·{z}^{3}\right)·\left(1,1,-1\right)=\left(2x·y·{z}^{3},{x}^{2}·{z}^{3},-3{x}^{2}·y·{z}^{2}\right)$At u=0, x=(1,1,-1) so ${D}_{u}f\left(x\right)=\left(2·1·1·-1,1·-1,-3·1·1·1\right)=\left(-2,-1,-3\right)$However, I'm not sure if this is correct as I don't know whether I'm meant to substitute u into f to find the derivative at a specific point or not? Kirsten Bishop 2022-11-24

## ${d}_{p}\left(x,y\right)=\sum _{n=1}^{N}|{x}_{n}-{y}_{n}{|}^{p}{\right)}^{\frac{1}{p}},p=\mathrm{\infty }$How can one intuitively understand the minkowski distance for $p=\mathrm{\infty }$? Brandon White 2022-11-23

## Let V be the solution space of the following homogeneous linear system:$\begin{array}{rl}{x}_{1}-{x}_{2}-2{x}_{3}+2{x}_{4}-3{x}_{5}& =0\\ {x}_{1}-{x}_{2}-{x}_{3}+{x}_{4}-2{x}_{5}& =0.\end{array}$Find dim(V) and a subspace W of ${\mathbb{R}}^{5}$ such that W contains V and $\mathrm{dim}\left(W\right)=4$. Justify your answer.Not sure how to go about doing this. piopiopioirp 2022-11-23
## Can I find length of bisector by knowing the position vectors?$\stackrel{\to }{A}$$\stackrel{\to }{B}$$\stackrel{\to }{C}$To find the length of angle bisector of bac I marked the points A(1,−1,−3) B(2,1,−2) C(−5,2,−6). How can I use the fact that the angle between the bisector and two adjacent sides is equal? Frankie Burnett 2022-11-21