A plane in R3 can be given by an equation Ax + By + Cz =...

A plane in R3 can be given by an equation Ax + By + Cz = D where A, B, C, and D areconstants and A, B, and C are not all zero. Suppose two planes are given by equations A1x+B1y+C1z = D1 and A2x+B2y+C2z = D2. The intersection of the two planes can be empty, or it can be a line, or the planes could be identical. How can the correct possibility be determined from the constants in the equations? Explain! (Hint: Think in terms of solving linear systems.)

Expert Solution

Colby Messinger answered 2 weeks ago

The distance between the parallel planes ax + by + cz + d1 = 0 and...

The distance between the parallel planes ax + by + cz + d1 = 0 and ax + by + cz + d2 = 0 is D = |d1 − d2| a2 + b2 + c2 . Find equations of the planes that are parallel to the plane x + 2y − 2z = 1 and three units away from it. (Enter your answers as a comma-separated list of equations.)

2.48. Is it true that {ax + by + cz|x, y, z ∈ Z} = {n...

2.48. Is it true that {ax + by + cz|x, y, z ∈ Z} = {n · gcd(a, b, c)|n ∈ Z}? 2.49. What are all the integer values of e for which the Diophantine equation 18x + 14y + 63z = e has an integer solution. Find a solution for each such e. 2.50. For integers a, b and k > 0, is it true that a | b iff a^k | b^k ?

Given the differential equation (ax+b)2d2y/dx2+(ax+b)dy/dx+y=Q(x) show that the equations ax+b=et and t=ln(ax+b) reduces this equation to...

Given the differential equation (ax+b)2d2y/dx2+(ax+b)dy/dx+y=Q(x) show that the equations ax+b=et and t=ln(ax+b) reduces this equation to a linear equation with constant coefficients hence solve (1+x)2d2y/dx2+(1+x)dy /dx+ y=(2x+3)(2x+4)

a) Find an equation of the plane tangent to the graph of f at the given point P.

a) Find an equation of the plane tangent to the graph of f at the given point P. Write your answer in the form ax + by +cz= d, where a, b, c, and d are integers with no common factor, and a is greater or equal to 0. f(x,y)= 2x3y + 4x-y, P(1,3,7) b) Use a multivariable chain rule to find a formula for the given derivative or partial derivative. w= f(x,y), x=g(u,v), y=h(u,v); ∂w/ ∂v

Find Cartesian equation of a plane through the point a and parallel to the given vectors...

Find Cartesian equation of a plane through the point a and parallel to the given vectors p and q. a = (1, - 1, 3) , p= ‹2, -1, 0›, q= ‹2, 0, 6›.

for the system equation of x' = Ax if Coefficients Matrix A be ? = [...

for the system equation of x' = Ax if Coefficients Matrix A be ? = [ 5 −5 −5 −1 4 2 3 −5 −3 ] , find the basic matrix

If an SPL ( LINEAR EQUATION SYSTEM ) is known: Ax = b. A is a...

If an SPL ( LINEAR EQUATION SYSTEM ) is known: Ax = b. A is a matrix sized m × n and b is a vector sized m × 1, with the component values of matrix A and vector b known. The x vector is n × 1 and the component values are unknown. Explain how the possible solution of SPL Ax = b. i want answer for the question , and what he mean by (the component values of...

Suppose A is an n × n matrix with the property that the equation Ax =...

Suppose A is an n × n matrix with the property that the equation Ax = b has at least one solution for each b in R n . Explain why each equation Ax = b has in fact exactly one solution

A power equation is a nonlinear regression equation of the form y equals ax Superscript by=axb....

A power equation is a nonlinear regression equation of the form y equals ax Superscript by=axb. Use a technology tool to find and graph the power equation for the data below. Include a scatter plot in your graph. Note that you can also find this model by solving the equation log y equals m left parenthesis log x right parenthesis plus blogy = m(log x)+b. LOADING... Click the icon to view the data set. x y 1 689 2 410...

2.) By Theorem 3.23 of the text, the linear diophantine equation of the form ax +...

2.) By Theorem 3.23 of the text, the linear diophantine equation of the form ax + by = c has no integral solutions if c is not divisible by (a, b), the greatest common divisor of a and b. On the other hand if (a, b) divides c, then we can use the Extended Euclidean Algorithm to find integers s, t such that sa + tb = (a, b); multiplying through by the correct factor gives an integral solution x,...

Question