Find the area of a plane R which has the vertices A(0, 0), B(2, 5), C(6, 3), D(4, -5), and E(0, -4)! Hint: Use the broad concept of determinant interpretation 1b. Find the equation of the plane that passes through the points A(2,0,2), B(0,4,4), and C(1,1,0)! Hint: Something to do with normal vectors! Use cross products and dot products.

Find the area of a plane R which has the vertices A(0, 0), B(2, 5), C(6, 3), D(4, -5), and E(0, -4)! Hint: Use the broad concept of determinant interpretation 1b. Find the equation of the plane that passes through the points A(2,0,2), B(0,4,4), and C(1,1,0)! Hint: Something to do with normal vectors! Use cross products and dot products.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: 1) If A = Find:- a) B2 5 -1-2 4 (2) -1 -2 and B = 3 b) determinant A c) Adjoint B d) A-¹

Q: Using the property of determinants, prove that |1 bc a(b+c)| 1 1 ab c(a+ b)| 2) ca b(c +a)| = 0

Q: Let A = [1 1 2 1 2 -3 5 4 L3 2 -1 1 -1 0 4] 6 and B = a) Find the determinant of A. b) Solve the…

A: Firstly, we will find the determinant by using row operations and then solve the given system of…

Q: Find the values of x, y, and z. (x y – z z z +3) +(y 4 3) = (4 8 16) (A x = 3, y = -9, z = 6 (Bx =…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: [1 1 5 2 1 21 (1) Let A = 0 2 B C =|1 3 l3 -1. I-2 3 -21 1. Calculate (if it possible): a) AXB. b)…

Q: (a) Let S be the parallelogram with vertices (3,0), (8, 1), (0,3), and (5, 4) in R2. Find the area…

Q: We wish to solve the system of linear equations by using Cramer's Rule. Begin by calculating the…

A: given system of equations

Q: Oppgåve 6. a) Find the determinant b) Find the determinant c) Find the determinant BITI 8 a 1 a +1 1…

Q: Find the determinant of A) -10 B) 0 C) 14 (D) 10 1 3 [42]

A: We can find the determinant as below

Q: Show that y = e", y = e2" , y = x and y = x² are linearly indepent functions %3D Hint: Use the…

A: To show y=ex,y=e2x,y=x,y=x2 are linearly independenr we are going to provethat the workian is…

Q: Calculating Cross Products with Determinants Find u X v and v X u if u 2i +j + k and v = -4i + 3j +…

Q: 4.) Find the Determinant Value and the variable x, & z? - x +2y -3z =1 2x + z = 0 3x -4y +4z = 2 %3D

Q: 1 -1 5) Let A= 1 0 -1 9-1 3 10 points a) Find A-. b) Find det(A), that is, the determinant of A.

Q: 2а 2b b - c 2b 2а а+c| %3D-2(а — b)?(а + b) а +b a+ b а

A: This is a determinant problem

Q: II. a. Find the area of the quadrilateral whose vertices are G4).-4).8) using determinant. ,29 and…

Q: Find the determinant in a) and b) where га CT f il det d e 7 %3D Lg_h а b C а C] а) А- 15g d f 5h…

A: Following are some results concerning determinant of a matrix. If we interchange any two rows, then…

Q: a) By using the property of the determinants prove that 1 + a? - b2 2ab -2b 1- a? + b? = (1 + a? +…

A: By using the properity of determinats prove that :

Q: Find the determinant: a) Using Pivotal Element Method only in all the steps b) Using Chio's…

A: Given:M = 07-7-5 661411-8-70-23 5-1341-63953 1

Q: 3.9. Let points A, B and C in the plane R2 have coordinates (x1, Y1), (x2, Y2) and (x3, Y3)…

A: Let,points A, B and C have coordinates (x1, y1), (x2, y2) and (x3, y3).To show:The area of triangle…

Q: Find a 3 x 3 determinant equation similar to that in Exercise 7 that describes the equation of the…

Q: Using the determinants, calculate the volume of the tetrahedron whose vertices are: A (2, 0, 1); B…

Q: 3] Use determinants to find the values of X, Y, Z, W, N. 8X - 3Y + Z + 5W – 4N = 21 5X + Y + 7Z -…

A: We have: 8X-3Y+Z+5W-4N=215X+Y+7Z-13W+15N=277X+3Y+4Z-18W-12N=3511X-7Y-Z+9W+15N=5015X+10Y-7Z+2W+8N=19…

Q: b) Use cofactor expansion along an appropriate row or column to compute he determinant of -20 B = 0…

Q: If Y is a 3x3 matrix and det(Y) = 5 then what is the determinant %3D of (-2)Y? a) -40 b) -10 c) -8…

Q: c) Let E = of course. 100 a 1 0 . Which one of the following matrices is the inverse of E? Justify…

A: We have to find the inverse of a matrix and justify the answer

Q: Use the determinant to compute the area of the parallelogram induced by the following two vectors:…

A: Given that v1→=-2.94.8, v2→=-0.4-8.6. Use the determinant to compute the area of the parallelogram…

Q: a' and b Expess the Vector paduct in from of de terminant: 2 = (2, a, as) 5= of where , (6, b, bs)…

Q: Consider the oystem dr * = da + 2y ; atby For the gioen junchon PLt) = (alt), y(t), determine )…

Q: 1.11 Show that the equation of a line in R² through (x₁, y₁) and (x2, y2) is given by this…

Question

1a. Find the area of a plane R which has the vertices A(0, 0), B(2, 5), C(6, 3), D(4, -5), and E(0, -4)!

Hint: Use the broad concept of determinant interpretation

1b. Find the equation of the plane that passes through the points A(2,0,2), B(0,4,4), and C(1,1,0)!

Hint: Something to do with normal vectors! Use cross products and dot products.

(2, 5)
4
(6, 3)
2
R
-2
6
-2
(0. -4)
(4, -5)
2.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

I need the answers of 4,5,6 and 7
.co Let T = a) 4 n, }] b) 4+n, The determinant of Tn is c) 4n², d) 4.
Can I get some help with this problem regarding determinants and two-dimensional coordinate geometry?
(6, 8) (1, 6) (8, 4) (-1, 3) (6, -2) Another approach for finding the area of a polygon by using determinants is to use the formula x3 In Yn 1 A = Y3 +.+ X1 Y1 X2 Y2 %3D Y2 C3 Y3 X4 Y4 Y1 (Xn,y,) are the n corner points in counterclockwise order. Use where (x,,y1), (X2,y2), the formula to compute the area of the polygon from the previous problem.
44 and 2) If the determinants B 2, find 12( AB)? (A.B are 4x4 matrices). a) 1/4 b) 8 c) 4 d) 2 e) 1/2
8. Determinants and lines Show that the lines x = a¡s + bj, y= a,s + bz, z = a3s + b3, -∞ < s < ∞ and x = ct + dị, y = c,t + dz, z = czt + dz, -00
Find u x v and show that it is orthogonal to both u and v. u = (-3, 0, 1) v = (8, -2, 0) The cross product of the vectors u = (u1, U2, u3) and v = (V1, V2, V3) is given by a determinant as k u x v = V1 V3
4) The determinant (det A) = abc, in the cases when A is: a y |b a)A = , b) A = 0 c) A = 0 d) b& c а a 0 у cl
Calculate: a) ABb) A’D’B’c) Find the determinant of D. Show all work
Please answer it with explanation in your own way. Please don't copy from Google. Otherwise i dislike it.