Given two planes 3x − 2y + z = 1 and 2x + y − 3z = 3.

Given two planes 3x − 2y + z = 1 and 2x + y − 3z = 3. (a). Find the equation for the line that is the intersection of the two planes. (b). Find the equation for the plane that is perpendicular to the two planes.

Expert Solution

milcah answered 2 years ago

Given two planes 3x − 2y + z = 1 and 2x + y − 3z...

Given two planes 3x − 2y + z = 1 and 2x + y − 3z = 3. (a). Find the equation for the line that is the intersection of the two planes. (b). Find the equation for the plane that is perpendicular to the two planes.

Solve: 4x - 3z = 1 -3x - z = -3 2x + y + z...

Solve: 4x - 3z = 1 -3x - z = -3 2x + y + z = -1

consider the following planes. -3x+y+z=3 18x-6y+3z=9 a.) find the angle between the two planes. (round your...

consider the following planes. -3x+y+z=3 18x-6y+3z=9 a.) find the angle between the two planes. (round your answer to two decimal places.) b.) find a set of parametric equation for the line of intersection of the planes. (use t for the parameter. enter you answers as a comma-separated list of equations)

Solve a. x + y = 3, 2x – y = 1 b. 3x + 2y = 6,...

Solve a. x + y = 3, 2x – y = 1 b. 3x + 2y = 6, x = 3 c. 2x + y = 4, y = -2x + 1 d. x – 3y = 6, 2x – y =1

Given two planes 2x - y + z = 7 and x + 3y - 4z...

Given two planes 2x - y + z = 7 and x + 3y - 4z = 1. (a) Give an orthogonal vector to each plane. (b) Do the planes intersect? Why or why not? (c) If they intersect, find the parametric equation of the intersection line, if not, find the distance of both planes.

solve by determinants a.x+y+z=0 3x-y+2z=-1 2x+3y+3z=-5 b. x+2z=1 2x-3y=3 y+z=1 c. x+y+z=10 3x-y=0 3y-2z=-3 d. -8x+5z=-19...

solve by determinants a.x+y+z=0 3x-y+2z=-1 2x+3y+3z=-5 b. x+2z=1 2x-3y=3 y+z=1 c. x+y+z=10 3x-y=0 3y-2z=-3 d. -8x+5z=-19 -7x+5y=4 -2y+3z=3 e. -x+2y+z-5=0 3x-y-z+7=0 -2x+4y+2z-10=0 f. 1/x+1/y+1/z=12 4/x-3/y=0 2/y-1/z=3

2. Given the System of Equations: 3x+2y+z+20w= 6 x+2y+z+10w=0 x+y+z+6w=2 2x+2y+z+15w=3 a) Use your calculator to...

2. Given the System of Equations: 3x+2y+z+20w= 6 x+2y+z+10w=0 x+y+z+6w=2 2x+2y+z+15w=3 a) Use your calculator to solve, leaving solution in parametric form b) Find the specific solution when y = 6 c) Perform, BY HAND, a full check of this particular solution

3. Solve the following system of equations. 5x- y+ z= -4 2x+ 2y-3z= -6 x-3y+ 2z=...

3. Solve the following system of equations. 5x- y+ z= -4 2x+ 2y-3z= -6 x-3y+ 2z= 0 Select the correct choice below: A. There is one solution. The solution is ( ). B. There are infinitely many solutions. The solutions ( ,z) C. There is no solution. 4. The total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a year is 150. The total number of these meals...

Consider the planes P1 : x + 2y − 3z = 3 and P2 : 4x...

Consider the planes P1 : x + 2y − 3z = 3 and P2 : 4x + y + z = 6. (a) Find a set of parametric equations for the line of intersection of the P1 and P2. (b) Find an equation in the standard for the plane that is perpendicular to the line of intersection of P1 and P2 (the one you found in part (a)) and contains the point A(3, −1, 2).

Consider a system of linear equations: x−y + 3z + u = 3 2x−2y + 7z...

Consider a system of linear equations: x−y + 3z + u = 3 2x−2y + 7z + u = 2 x−y + 2z + u = 1 1. Write down the augmented matrix of the system, and take this matrix to the reduced row echelon form. 2. Determine the leading and the free variables of the system, and write down its general solution.

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