Can anyone please help me to solve this problem I am stuck! **Title: Calculating the Cross Product of Vectors**To find the cross product of two vectors **a** and **b**, given:**a** = ⟨-3, -5, 6⟩ **b** = ⟨-4, 3, -7⟩The cross product **a × b** is calculated using the determinant of a 3x3 matrix:\[\mathbf{a \times b} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \end{vmatrix}\]Where:- \( \mathbf{i}, \mathbf{j}, \mathbf{k} \) are the unit vectors in the x, y, and z directions.- \( a_1, a_2, a_3 \) are the components of vector **a**.- \( b_1, b_2, b_3 \) are the components of vector **b**.Substitute the given values:\[\mathbf{a \times b} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ -3 & -5 & 6 \\ -4 & 3 & -7 \end{vmatrix}\]Compute the determinant:\[\mathbf{a \times b} = \mathbf{i} (-5 \cdot -7 - 6 \cdot 3) - \mathbf{j} (-3 \cdot -7 - 6 \cdot -4) + \mathbf{k} (-3 \cdot 3 - (-5) \cdot -4)\]Calculate each component:1. **i**: \((-5 \times -7) - (6 \times 3) = 35 - 18 = 17\)2. **j**: \((-3 \times -7) - (6 \times -4) = 21 + 24 = 45\)3. **k**: \((-3 \times 3) - (-5 \times -4) = -9 - 20 = -29\)Thus, the cross product **a × b** is ⟨17, -45, **Cross Product Calculation****Problem Statement:**Find the cross product \( \mathbf{a} \times \mathbf{b} \).**Vectors:**- \( \mathbf{a} = \langle -3, -5, 0 \rangle \)- \( \mathbf{b} = \langle 4, 3, -7 \rangle \)**Calculation:**To find the cross product of two vectors \( \mathbf{a} \) and \( \mathbf{b} \), we use the following determinant formula:\[\mathbf{a} \times \mathbf{b} = \begin{vmatrix}\mathbf{i} & \mathbf{j} & \mathbf{k} \\-3 & -5 & 0 \\4 & 3 & -7 \end{vmatrix}\]Which expands to:\[= \mathbf{i}((-5)(-7) - (0)(3)) - \mathbf{j}((-3)(-7) - (0)(4)) + \mathbf{k}((-3)(3) - (-5)(4))\]Calculate each component:- \(\mathbf{i}\) component: \(= 35 - 0 = 35\)- \(\mathbf{j}\) component: \(= 21 - 0 = 21\)- \(\mathbf{k}\) component: \(= -9 + 20 = 11\)Thus, the cross product is:\[\mathbf{a} \times \mathbf{b} = \langle 35, -21, 11 \rangle\]

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Answered: Find the cross product axb 6=(-4,3-5)…

Find the cross product axb 6=(-4,3-5) Where a= (-3, -5,0) and (483 axb =

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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