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If r = (4, -2, 2) and F = (4, 8, 4), what is r x F?

If r = (4, -2, 2) and F = (4, 8, 4), what is r x F?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Question**: If r = (4, -2, 2) and F = (4, 8, 4), what is r x F? This text appears to be a mathematical question focusing on vector cross product. The query asks for the cross product (denoted as "x") of two vectors \( r \) and \( F \). ### Explanation of Vectors and the Cross Product: Vectors are fundamental to the study of physics, engineering, and computer science. In three-dimensional space, a vector is typically represented as \((x, y, z)\), where \( x \), \( y \), and \( z \) are its components along the respective axes. The cross product of two vectors \( \mathbf{a} = (a_1, a_2, a_3) \) and \( \mathbf{b} = (b_1, b_2, b_3) \), results in a vector that is perpendicular to both \( \mathbf{a} \) and \( \mathbf{b} \). The resulting vector \( \mathbf{c} \) can be found using the determinant of a matrix as follows: \[ \mathbf{a} \times \mathbf{b} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ \end{vmatrix} \] Expanding this determinant, we get: \[ \mathbf{a} \times \mathbf{b} = \left((a_2b_3 - a_3b_2)\mathbf{i} - (a_1b_3 - a_3b_1)\mathbf{j} + (a_1b_2 - a_2b_1)\mathbf{k}\right) \] ### Given Vectors: - \( r = (4, -2, 2) \) - \( F = (4, 8, 4) \) ### Calculating the Cross Product: Using the formula above: \[ \mathbf{r} \times \mathbf{F} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 4 & -2 & 2 \\ 4 & 8 &
Transcribed Image Text:**Question**: If r = (4, -2, 2) and F = (4, 8, 4), what is r x F? This text appears to be a mathematical question focusing on vector cross product. The query asks for the cross product (denoted as "x") of two vectors \( r \) and \( F \). ### Explanation of Vectors and the Cross Product: Vectors are fundamental to the study of physics, engineering, and computer science. In three-dimensional space, a vector is typically represented as \((x, y, z)\), where \( x \), \( y \), and \( z \) are its components along the respective axes. The cross product of two vectors \( \mathbf{a} = (a_1, a_2, a_3) \) and \( \mathbf{b} = (b_1, b_2, b_3) \), results in a vector that is perpendicular to both \( \mathbf{a} \) and \( \mathbf{b} \). The resulting vector \( \mathbf{c} \) can be found using the determinant of a matrix as follows: \[ \mathbf{a} \times \mathbf{b} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ \end{vmatrix} \] Expanding this determinant, we get: \[ \mathbf{a} \times \mathbf{b} = \left((a_2b_3 - a_3b_2)\mathbf{i} - (a_1b_3 - a_3b_1)\mathbf{j} + (a_1b_2 - a_2b_1)\mathbf{k}\right) \] ### Given Vectors: - \( r = (4, -2, 2) \) - \( F = (4, 8, 4) \) ### Calculating the Cross Product: Using the formula above: \[ \mathbf{r} \times \mathbf{F} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 4 & -2 & 2 \\ 4 & 8 &
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