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.

Expert Solution

Colby Messinger answered 2 years ago

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.) °

The reflection of the plane 2x-3y+4z-3=0 in the plane x-y+z-3=0 is the place

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.

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.

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

Consider the following planes. 5x − 3y + z = 2, 3x + y − 5z...

Consider the following planes. 5x − 3y + z = 2, 3x + y − 5z = 4 (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.)

The vector field given by E (x,y,z) = (yz – 2x) x + xz y +...

The vector field given by E (x,y,z) = (yz – 2x) x + xz y + xy z may represent an electrostatic field? Why? If so, finding the potential F a from which E may be obtained.

Solve for x,y,z using the inverse if possible. x+2y+5z=2 2x+3y+8z=3 -x+y+2z=3

Find the equation of the plane through the point (1,1,1) which is perpendicular to the line of intersection of the two planes x−y−3z=−1 and x−3y+z= 2.

Determine whether the following two planes x + 4y − z = 7 and 5x −...

Determine whether the following two planes x + 4y − z = 7 and 5x − 3y −7z = 11 are parallel, orthogonal, coincident (that is, the same) or none of these. please show full working for learning purposes

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