3. Among all the points on the graph of z = 10 – x² – y² above the plane x + 2y + 3z = 0, find the point farthest from the plane.

Q: 11) Find the equation of the plane that passes through the point (1, 5, 1) and is perpendicular to…

A: A plane is passing through a point (1,5,1) and is perpendicular to the planes 2x + y - 2z = 2 and x+…

Q: 2-) Find the Symmetric form of the equation of the line of in tersection of the two Planes X- +Z =2,…

A:

Q: Of all the points on the graph of z = 10 - x^2 - y^2 that lie above the plane x + 2y + 3z = 0, what…

A:

Q: 9. Find the equations of the planes that are parallel to 2.x - 2y + z = 5 such that the distance…

A: We will solve the problem.

Q: 2. Find the distance of the point A : (1,0, 2) from the plane P: 3x +y+ z = 9.

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

Q: Calculate , z² dS if S is the prism whose base is the triangle in the limited xy plane by the x axis…

A: Here given figure is Since prism has 5 surfaces (1)-OAB (2) OADE (3) CDE (4) OBCD (5) ABCE

Q: (1) Find an equation for the plane that passes through the point (–1,2,2) and contains the line of…

A: Given: Equation of planes x+y-z=5⇒x+y-z-5=0 and 3x-y+5z=3⇒3x-y+5z-3=0 and point -1,2,2, To find: The…

Q: Determine the point on the plane 2x + 3y − 4z = 0 that is closest to the point P(1, 1, 1)

A:

Q: Above the paraboloid z= 6-x-y² and under the plane z= 9 for x? +y? < 4 .

A: volume by double integral using  polar coordinate

Q: 23. The distance of the origin from the plane 2x – 3y + 6z = 14 is A 2 В 14 C с -2 D -14

A: on solving that we get

Q: Find a plane through P (2, 1, 1) and perpendicular to the line of intersec- tion of the planes:…

A: find a plane through P2,1,1 and perpendicular to the line of intersection of the planes  2x+y-z=3 ,…

Q: Find the point on the plane x-y+z=7 that is closest to the point (2,4,6).

A:

Q: b. Find the distance from the point (2, –2, 3) to the intersection of the planes 2x – y + 3z = 1 and…

A:

Q: 4. Find a plane through Po(2, 1, –1) and perpendicular to the line of in- tersection of the planes…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the distance (d) from the point (– 6, – 8, – 7) to the plane 5x – 2y + 2z = 25. - d =

A:

Q: 5. Among all the points on the graph of z = 10 – x² – y² that lie above the plane r+2y +3z = 0, find…

A:

Q: 45. Find the distance from the plane x + 2y + 6z = 1 to the plane x + 2y + 6z = 10.

A:

Q: The plane containing the point (2,5,0) and parallel to the plane 3x – 7y + 6z = 8 has equation Ах +…

A: Recall:      The equation of the plane parallel to Ax+By+Cz=D and passes through the point  α,β,γ ,…

Q: A. Show that the planes (x+y- z = 1) and ( 2x - 3y + 4z = 5 ) are neither parallel nor…

A: Let's find.

Q: find the equation of the plane with the given description. Passes through O and is parallel to 4x −…

A: Solution:Given    A plane 4x − 9y + z = 3To find the equation of the plane passess through O and is…

Q: The plane 6x + 8y + 60z = 700 intersects th of the highest and lowest points or coordinates

A: Given that the plane           6x+8y+60z=700  and the cone                            z2=x2+y2

Q: Find the point Q symmetric to the point P (1; 3; —4) with respect to the plane 3x+y-2z=0

A:

Q: (31) Find a plane through A(2, 1, –1) and perpendicular to the line of intersection of the planes 2x…

A: Given, 2x+y-z=3 ,x+2y+z=2 The equation of the plane passing through x1,y1,z1 is given by…

Q: 7. If 1x, y2 are the coordinates of a point P in the xy-plane,then x is called the__________________…

A: Given that, x,y are the coordinates of a point P in the xy-plane. The objective is to fill in the…

Q: Among all the points on the graph of z = 10 − x2 − y2 that lie above the plane x+ 2y + 3z= 0, find…

A: We have, z = 10 - x2 - y2 and equation of plane is , x + 2y + 3z = 0 The required point on z = 10 -…

Q: 39. The plane that passes through the point (1, 5, 1) and is perpendicular to the planes 2x +y - 2z…

A:

Q: Find the equation of the plane that contains point P(1, -1, 2) and has the normol n= 2¿+3j+Sk.

A:

Q: If the image of the point (1 -2 3) in the plane 2x+3y-z=7 is the point x, y, z then the value of…

A: Let's first understand the

Q: 9. Find the equation of the plane through P(1,1,4) that is parallel to the plane x+ 5y – z + 8 = 0

A: The scalar equation of parallel planes differ only by a constant Therefore, equation of the required…

Q: 10. The distance between the point (3,-2,5) and the plane 2x+2y+z=5 is NONE

A: Given: The distance between (3,-2,5) and the plane 2x+2y+z=5

Q: 4. Find an equation for the plane in R³ spanned by the points (1,5, 1) and (1, 4, 2).

A: The two vectors are given as v1 = 151v2 = 142 Let xyz∈span{v1 , v2} Then xyz = mv1+nv2= m151+n142=…

Q: 5) Given the point Q(2, 0, 1) and a plane p: 3x + y - 4z = 24, Find the distance from Q to p.

A:

Q: 39. The plane that passes through the point (1, 5, 1) and is perpendicular to the planes 2x + y – 2z…

A: Given:

Q: Evaluate ||x'y dA if D is the triangle in the xy-plane with vertices at (0,0), (5,2), and (0,2).

A:

Q: Among all the points on the graph of z = 10-x2 -y² that lie above the plane r+2y+3z = 0, ind the…

A: Given that z=10-x2-y2 and x+2y+3z=0 Find the point which is farthest from the plane.

Q: d the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10

A:

Q: the

A: We will find the distance.

Q: 5. Find a plane through the points P(1,2, 3), P2(3, 2, 1) and perpendicu- lar to the plane 4x – y+…

A:

Q: 6) = Find the point at which the line intersects the given plane. x =3 - t, y = 2 + t, z = 5t; x - y…

A: Equation of a Line in Parametric Form: where are functions of and is the parameter The equation of…

Q: Find the shortest distance between (3,4,1 ) and the plane X+y +Z = -2

A: Using distance between plane and point formula we can calculate.

Q: 4) Find the distance from the point (1, 2, – 1) to the plane 2x+y- 2z = 1.

A:

Q: Find the point on the graph of z = x2 + y2 + 10 nearest the plane x + 2y - z = 0.

A:

Q: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot the…

Q: +4z=8 and

A: The equation of the plane as, x+z=1orx+0y+z=1 Here, a1 =1,b1 =0,c1 =1. and x+2y+4z=8 Here, a2 =1,b2…

Q: 12. Find the distance between the point (3,-2,7) and the plane 4x – 6 y + z = 5.

A: The equation of plane is 4x-6y+z=5 and the given point is 3,-2,7. The distance between the point and…

Q: The plane containing the point (-4,1,3) and parallel to the plane 4x + 7y – 3z = 2 has equation Ar +…

A:

Q: Q2) Find the distance from the point P (1, 2, 3) to the plane x-3y + 2z= 4.

A:

Q: Find the point on the plane 3x+4y+z=8that is nearest to​ (2,0,1). What are the values of​ x, y,…

A:

Q: Among all the points on the graph of z = 10 - x2 - y2 that lie above the plane x + 2y + 3z = 0, find…

A:

Q: Find the points PCo10,0),Q Ce,2,0) and RCOl- thal- 2I to the line: the Line in the Plane of passes…

A: