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).

Expert Solution

milcah answered 2 years ago

P1=4x-z-3, p2=x+2y+z a) The two planes P1 and P2 will intersect in a line. Find the...

P1=4x-z-3, p2=x+2y+z a) The two planes P1 and P2 will intersect in a line. Find the Cartesian coordinate of the point at which the two planes P1 and P2 intersect and x = 0 b) find the vector equation of a line which is the intersection of the two planes P1 and P2.

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.

Consider the following planes. x + y + z = 7, x + 3y + 3z =...

Consider the following planes. x + y + z = 7, x + 3y + 3z = 7 (a) Find parametric equations for the line of intersection of the planes. (Use the parameter t.) (x(t), y(t), z(t)) = (b) Find the angle between the planes. (Round your answer to one decimal place.) °

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.

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.

Question 5 Find all solutions of this system. 4x + 2y + 3z = 0 3x...

Question 5 Find all solutions of this system. 4x + 2y + 3z = 0 3x y + 2z = 0 x + 2y − z = 0 Compare the value of the determinant of the coefficient matrix to zero using the nature of the solution.

. Consider this hypothesis test: H0: p1 - p2 = < 0 Ha: p1 - p2...

. Consider this hypothesis test: H0: p1 - p2 = < 0 Ha: p1 - p2 > 0 Here p1 is the population proportion of “happy” of Population 1 and p2 is the population proportion of “happy” of Population 2. Use the statistics data from a simple random sample of each of the two populations to complete the following: Population 1 Population 2 Sample Size (n) 1000 1000 Number of “yes” 600 280 a. Compute the test statistic z. b....

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)

1. Consider this hypothesis test: H0: p1 - p2 = < 0 Ha: p1 - p2...

1. Consider this hypothesis test: H0: p1 - p2 = < 0 Ha: p1 - p2 > 0 Here p1 is the population proportion of “happy” of Population 1 and p2 is the population proportion of “happy” of Population 2. Use the statistics data from a simple random sample of each of the two populations to complete the following: Population 1 Population 2 Sample Size (n) 1000 1000 Number of “yes” 600 280 a. Compute the test statistic z. b....

Consider this hypothesis test: H0: p1 - p2 = 0 Ha: p1 - p2 > 0...

Consider this hypothesis test: H0: p1 - p2 = 0 Ha: p1 - p2 > 0 Here p1 is the population proportion of “yes” of Population 1 and p2 is the population proportion of “yes” of Population 2. Use the statistics data from a simple random sample of each of the two populations to complete the following: (8 points) Population 1 Population 2 Sample Size (n) 500 700 Number of “yes” 400 560 Compute the test statistic z. What is...

Question