Learn Vectors with Examples, Equations, and Practice Problems

If $A = - a_{x} + 6 a_{v} + 5 a_{z} a n d B = a_{x} + 2 a_{y} + 3 a_{x}$ , find the vector projection of B on A

balafiavatv 2022-08-08

If $A = 5 a_{x} + 3 a_{y} + 2 a_{z}$
$B = - a_{x} + 4 a_{y} + 6 a_{z}$
$C = 8 a_{x} + 2 a_{y}$
find the values of $α$ and $β$ such that $α A + β B + C$ is parallel to the y-axis.

Jaylyn Gibson 2022-08-07

Find the cross product $a \times b$ and verify that it is orthogonal to both a and b.
a = j + 7k
b = 2i - j +4k

pleitatsj1 2022-08-07

Let $v_{1}, . . ., v_{n}$ be linealy independent vectors in $R^{m}$ and let $w = a_{1} v_{1} + . . . + a_{n} v_{n}$ with real numbers $a_{1}, . . . a_{n}$ , be linear combination of these vectors.
Prove if $a_{1} \neq 0$ , then the vector $w, v_{2}, . . ., v_{n}$ are linearly independent
So far, what I have thought is forming a formula like this: $x_{1} w + x_{2} v_{2} + . . . + x_{n} v_{n} = 0$ , because $v_{1}, . . ., v_{n}$ is linearly independent vectors, so $x_{2} = . . . = x_{n} = 0$ , then now we need to prove $x_{1} = 0$ so these vector will be linearly independent. But from here, I don't know how to process further more in this problem, can anyone help me out with a way to solve this or a better alternative solution is appreciate.

Jaylyn Gibson 2022-08-07

How do I find a constant B>0, so that $‖ x ‖$ $\leq$ $B * {‖ x ‖}_{\infty}$ works for all $x \in R^{n}$ ?
Not sure but I think I have to look at $x$ = $\sum_{i = 1}^{n} x_{i} e_{i}$ with the development of the x to the canonical unit vectors $e_{i}$ . But how do I do that?

rivasguss9 2022-08-06

Let a & b be non-zero vectors such that $a \cdot b = 0$ . Use geometric description of scalar product to show that a & b are perpendicular vectors.
What I've done so far is to state that $\cos 90$ (i.e. perpendicular) gives 0 which would make the rest of the equation $| a | | b | \cos θ = 0$

Bierlehre59 2022-08-06

Let $A$ be a matrix and $x$ be a non-zero vector such that $A x = 2 x .$
Then we have that $A^{7} x = a x$ some value of a. What is a equal to?
I know I need to start by finding "A" but I'm not sure how. And will I need to do v by multiplying "A" seven times or is there a faster way?

Marco Hudson 2022-08-05

Find the scalar and the vector projections of vector b onto the direction of vector a, where a = [0, -2, -16] and b = [12, -16, -18].

musicbachv7 2022-08-05

Find the values of x such that the vectors $a = [- 32 x, - 26, - 32 x^{2}] a n d b = [- 38, - 29, 5]$ are orthogonal.

Yair Valentine 2022-08-04

A point is located 7 units in front of the yz plane, 2 units toleft of xz plane, and one unit below the xy plane. What are the coordinates of the point?

Nina Bean 2022-08-02

Give the components of the velocity vector for wind blowing at 14 km/hr toward the southeast. (Assume north is the positivey-direction.) Give the componets in exact form.

Aphroditeoq 2022-08-01

$Find the normal line to the plan A x + B y + C z + d = 0 that passes through the point x_{0}, y_{0}, z_{0}$

ganolrifv9 2022-07-31

u=7i+3j+5k
v=-8i+4j+2k
determine if the 2 vectors make an acute angle, obtuse angle, or are orthogonal.

Cristofer Graves 2022-07-30

E and F are vector fields given by $E = 2 x a_{x} + a_{y} + y z a_{z}$ and $F = x y a_{x} - y^{2} a_{y} + x y z a_{z}$ .
Determine:
(a)|E| at (1,2,3)

przesypkai4 2022-07-30

Find the length and direction of $u \times v$ and $v \times u$
u = 2i - 2j + 4k, v = -i + j - 2k

Avery Stewart 2022-07-27

Simplify
(5+j4)(3+j7)(2-j3)

ganolrifv9 2022-07-27

Find the unit vectors that are parallel to the tangent line to the parabola $y = x^{2}$ at the point (2,4)

Patricia Bean 2022-07-26

Show algebraically that a triangle cannot be drawn with vertices at the three points A(2, 5), B(6, 1), and C(8, -1). There are (at least) two distinct approaches to this problem.

Bernard Boyer 2022-07-25

Given that $A = 3 a_{x} + 5 a_{y} - 7 a_{z} a n d B = a_{x} - 2 a_{y} + a_{z}$ , find:
$(a) | 2 B + 0.4 A |, (b) A * B - | B |^{2}, (c) A \times B$

Ismael Molina 2022-07-25

If $A = - a_{x} + 6 a_{y} + 5 a_{z} a n d B = a_{x} + 2 a_{y} + 3 a_{x}$ , find (a) the scalar projection of A on B

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

Vector Examples, Equations, and Practice Problems