𝐮=2 𝐢+3 𝐣-4 𝐤, 𝐯=-3 𝐢+𝐣-4 𝐤 𝐰=𝐢+𝐣-3 𝐤. Find the following. 𝐮 ×(-𝐯)

Name: Problem 28, Chapter 10: Calculus, Early Transcendentals
Uploaded: 2021-08-08T14:31:48-08:00
Duration: 1 min 11 s
Channel: Monica Miller
Description: 𝐮=2 𝐢+3 𝐣-4 𝐤, 𝐯=-3 𝐢+𝐣-4 𝐤 𝐰=𝐢+𝐣-3 𝐤. Find the following. 𝐮 ×(-𝐯)

step 1 Okay, we're going to find the cross product between U and then the negative of V. So let's go ah

Question

$\mathbf{u}=2 \mathbf{i}+3 \mathbf{j}-4 \mathbf{k}, \mathbf{v}=-3 \mathbf{i}+\mathbf{j}-4 \mathbf{k}$ $\mathbf{w}=\mathbf{i}+\mathbf{j}-3 \mathbf{k}$. Find the following. $\mathbf{u} \times(-\mathbf{v})$

   $\mathbf{u}=2 \mathbf{i}+3 \mathbf{j}-4 \mathbf{k}, \mathbf{v}=-3 \mathbf{i}+\mathbf{j}-4 \mathbf{k}$
$\mathbf{w}=\mathbf{i}+\mathbf{j}-3 \mathbf{k}$. Find the following.
 $\mathbf{u} \times(-\mathbf{v})$

Calculus, Early Transcendentals

Michael Sullivan,… 1st Edition

Chapter 10, Problem 28

Instant Answer

Solved by Expert Monica Miller

08/08/2021

Step 1

Step 1: First, we need to distribute the negative sign into the vector $\mathbf{v}$, which gives us $\mathbf{-v} = 3\mathbf{i} - \mathbf{j} + 4\mathbf{k}$. Show more…

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$\mathbf{u}=2 \mathbf{i}+3 \mathbf{j}-4 \mathbf{k}, \mathbf{v}=-3 \mathbf{i}+\mathbf{j}-4 \mathbf{k}$ $\mathbf{w}=\mathbf{i}+\mathbf{j}-3 \mathbf{k}$. Find the following. $\mathbf{u} \times(-\mathbf{v})$

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Key Concepts

Vector Cross Product

The vector cross product is an operation on two vectors in three-dimensional space, resulting in a new vector that is perpendicular to the plane containing the original vectors. The magnitude of the cross product corresponds to the area of the parallelogram formed by the two vectors, and its direction is determined by the right-hand rule. This concept is essential in physics and engineering when dealing with torques, rotational motion, and magnetic forces.

Component Representation of Vectors

Vectors in three dimensions are often expressed in terms of their components along the i, j, and k (or x, y, and z) axes. This representation simplifies operations like addition, scalar multiplication, and the cross product by allowing each operation to be performed component-wise using algebraic methods such as the determinant method for computing the cross product.

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