Learn Vectors with Examples, Equations, and Practice Problems

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)

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 $\vec{A}$ 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 $\vec{A}$ and $2 \vec{i} + \vec{j} - 2 \hat{k}$

Jaelyn Mueller 2023-02-18

How to find a unit vector normal to the surface $x^{3} + y^{3} + 3 x y z = 3$ ay the point(1,2,-1)?

FeelryclurN9g3z 2023-02-16

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

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)?

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 ${\vec{w}}_{1} = (2, 3)$ and ${\vec{w}}_{2} = (1, 1)$ , but they are relative to the basis $\vec{u} = (1, 1), \vec{v} = (1, - 1)$ . 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 $f = x^{2} \cdot y \cdot z^{3}$ along the curve $x = e^{- u}; y = 2 \sin u + 1; z = u - \cos u$ 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 $D_{u} f (x) = \nabla f (x) \cdot u = (2 x \cdot y \cdot z^{3}, x^{2} \cdot z^{3}, 3 x^{2} \cdot y \cdot z^{3}) \cdot (1, 1, - 1) = (2 x \cdot y \cdot z^{3}, x^{2} \cdot z^{3}, - 3 x^{2} \cdot y \cdot z^{2})$
At u=0, x=(1,1,-1) so $D_{u} f (x) = (2 \cdot 1 \cdot 1 \cdot - 1, 1 \cdot - 1, - 3 \cdot 1 \cdot 1 \cdot 1) = (- 2, - 1, - 3)$
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?

Kirsten Bishop 2022-11-24

$d_{p} (x, y) = \sum_{n = 1}^{N} | x_{n} - y_{n} |^{p})^{\frac{1}{p}}, p = \infty$
How can one intuitively understand the minkowski distance for $p = \infty$ ?

Brandon White 2022-11-23

Let V be the solution space of the following homogeneous linear system:
$\begin{aligned} x_{1} - x_{2} - 2 x_{3} + 2 x_{4} - 3 x_{5} & = 0 \\ x_{1} - x_{2} - x_{3} + x_{4} - 2 x_{5} & = 0. \end{aligned}$
Find dim(V) and a subspace W of $R^{5}$ such that W contains V and $\dim (W) = 4$ . 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?
$\vec{A}$
$\vec{B}$
$\vec{C}$
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

The question is the following:
Given the curve $r (a) =< 6 - a^{2}, a^{3} + 1, 1 - a >$ and the plane $x + y + z = π$ , 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 $T (a) = \frac{< - 2 a, 3 a^{2}, - 1 >}{\sqrt{(- 2 a)^{2} + (3 a^{2})^{2} + (- 1)^{2}}}$ . 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.

Precalculus

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Vector Examples, Equations, and Practice Problems