Recent questions in Vectors

PrecalculusAnswered question

Riley Barton 2023-03-29

Find, correct to the nearest degree, the three angles of the triangle with the given vertices

A(1, 0, -1), B(3, -2, 0), C(1, 3, 3)

A(1, 0, -1), B(3, -2, 0), C(1, 3, 3)

PrecalculusAnswered question

Audrey Hall 2023-03-25

How to find the angle between the vector and $x-$axis?

PrecalculusAnswered question

imbustatozyd6 2023-02-25

How to find a unit vector with the same direction as 8i - j + 4k?

PrecalculusAnswered question

Admiddevadxvi 2023-02-21

Let $\overrightarrow{A}$ be vector parallel to line of intersection of planes ${P}_{1}$ and ${P}_{2}$ through origin. ${P}_{1}$ is parallel to the vectors $2\hat{j}+3\hat{k}$ and $4\hat{j}-3\hat{k}$ and ${P}_{2}$ is parallel to $\hat{j}-\hat{k}$ and $3\hat{i}+3\hat{j}$ then the angle between vector $\overrightarrow{A}$ and $2\overrightarrow{i}+\overrightarrow{j}-2\hat{k}$

PrecalculusAnswered question

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)?

PrecalculusAnswered question

FeelryclurN9g3z 2023-02-16

How do I find the magnitude and direction angle of the vector $v=3i-4j$?

PrecalculusAnswered question

Elaina Mullen 2023-02-09

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

PrecalculusAnswered question

Maxwell Mccoy 2022-12-15

A quantity which has both magnitude and direction is called ______.

PrecalculusAnswered question

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?

PrecalculusAnswered question

valahanyHcm 2022-11-26

Which one of the following is a vector quantity?

A)Distance

B)Displacement

C)Position

D)Speed

A)Distance

B)Displacement

C)Position

D)Speed

PrecalculusAnswered question

gheadarce 2022-11-24

If I have ${\overrightarrow{w}}_{1}=(2,3)$ and ${\overrightarrow{w}}_{2}=(1,1)$, but they are relative to the basis $\overrightarrow{u}=(1,1),\overrightarrow{v}=(1,-1)$. How do I find the scalar product of ${w}_{1}$ and ${w}_{2}$?

I know that $\u27e8{w}_{1},{w}_{2}\u27e9=2\cdot 1+3\cdot 1$ 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?

I know that $\u27e8{w}_{1},{w}_{2}\u27e9=2\cdot 1+3\cdot 1$ 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?

PrecalculusAnswered question

Salvador Whitehead 2022-11-24

Find the directional derivative of $f={x}^{2}\xb7y\xb7{z}^{3}$ along the curve $x={e}^{-u};\text{}\text{}\text{}\text{}y=2\mathrm{sin}u+1;\text{}\text{}\text{}\text{}z=u-\mathrm{cos}u$ at the point P where u = 0

My working:

At u=0, x=1, y=1, z=-1 so let u = (1,1,-1).

Know that ${D}_{u}f(x)=\nabla f(x)\xb7u=(2x\xb7y\xb7{z}^{3},{x}^{2}\xb7{z}^{3},3{x}^{2}\xb7y\xb7{z}^{3})\xb7(1,1,-1)=(2x\xb7y\xb7{z}^{3},{x}^{2}\xb7{z}^{3},-3{x}^{2}\xb7y\xb7{z}^{2})$

At u=0, x=(1,1,-1) so ${D}_{u}f(x)=(2\xb71\xb71\xb7-1,1\xb7-1,-3\xb71\xb71\xb71)=(-2,-1,-3)$

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?

My working:

At u=0, x=1, y=1, z=-1 so let u = (1,1,-1).

Know that ${D}_{u}f(x)=\nabla f(x)\xb7u=(2x\xb7y\xb7{z}^{3},{x}^{2}\xb7{z}^{3},3{x}^{2}\xb7y\xb7{z}^{3})\xb7(1,1,-1)=(2x\xb7y\xb7{z}^{3},{x}^{2}\xb7{z}^{3},-3{x}^{2}\xb7y\xb7{z}^{2})$

At u=0, x=(1,1,-1) so ${D}_{u}f(x)=(2\xb71\xb71\xb7-1,1\xb7-1,-3\xb71\xb71\xb71)=(-2,-1,-3)$

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?

PrecalculusAnswered question

Kirsten Bishop 2022-11-24

${d}_{p}(x,y)=\sum _{n=1}^{N}|{x}_{n}-{y}_{n}{|}^{p}{)}^{\frac{1}{p}},p=\mathrm{\infty}$

How can one intuitively understand the minkowski distance for $p=\mathrm{\infty}$?

How can one intuitively understand the minkowski distance for $p=\mathrm{\infty}$?

PrecalculusAnswered question

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 $\mathrm{dim}(W)=4$. Justify your answer.

Not sure how to go about doing this.

$\begin{array}{rl}{x}_{1}-{x}_{2}-2{x}_{3}+2{x}_{4}-3{x}_{5}& =0\\ {x}_{1}-{x}_{2}-{x}_{3}+{x}_{4}-2{x}_{5}& =0.\end{array}$

Find dim(V) and a subspace W of ${\mathbb{R}}^{5}$ such that W contains V and $\mathrm{dim}(W)=4$. Justify your answer.

Not sure how to go about doing this.

PrecalculusAnswered question

piopiopioirp 2022-11-23

Can I find length of bisector by knowing the position vectors?

$\overrightarrow{A}$

$\overrightarrow{B}$

$\overrightarrow{C}$

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?

$\overrightarrow{A}$

$\overrightarrow{B}$

$\overrightarrow{C}$

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?

PrecalculusAnswered question

Frankie Burnett 2022-11-21

The question is the following:

Given the curve $r(a)=<6-{a}^{2},{a}^{3}+1,1-a>$ and the plane $x+y+z=\pi $, find all the points where the tangent vector on r(a) is parallel to the plane.

I know finding the tangent vector is the first part of the problem. That would be $T(a)=\frac{<-2a,3{a}^{2},-1>}{\sqrt{(-2a{)}^{2}+(3{a}^{2}{)}^{2}+(-1{)}^{2}}}$. But beyond there I don't know how to draw a relationship between the line and plane.

Given the curve $r(a)=<6-{a}^{2},{a}^{3}+1,1-a>$ and the plane $x+y+z=\pi $, find all the points where the tangent vector on r(a) is parallel to the plane.

I know finding the tangent vector is the first part of the problem. That would be $T(a)=\frac{<-2a,3{a}^{2},-1>}{\sqrt{(-2a{)}^{2}+(3{a}^{2}{)}^{2}+(-1{)}^{2}}}$. But beyond there I don't know how to draw a relationship between the line and plane.

Vectors in the Precalculus course are usually more challenging since there are different vectors examples that are always mentioned. For example, if you are majoring in Engineering disciplines, you will have to use more than one approach to explain the most efficient ways. Take a look at vectors practice problems that have been presented below. It will help you learn and find the answers that will let you see the best equation and graphs. At the same time, when you are dealing with vectors equations, do not forget about unknown coefficients as you are looking for combinations and various solutions.