8) Find equations of (a) the tan gent plane and (b) the normal line to the given surface at the specified point. 2(x- 2)^2+(y-1)^2+(z-3)^2=10,(3,3,5)

Q: 1 Find equation of plane which is containing Points A(2,1,1) and B(7,5,2) and normal to 2 x - 3y -…

A: We have to find the required plane

Q: 15. Perpendicular to the plane x + 3y – z-7=0 and containing the points (2,0, 5) and (0, 2, -

A:

Q: Find parametric equations for the normal line to the surface z=-7x2 -9y2   at the point   (2,1,-37)

A:

Q: 9. Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

A:

Q: Find parametric equations of the line through the point (8, 3, 4) that is parallel to the plane -2x…

A: First find vector normal to plane Write equation of line

Q: Find a vector equation of the normal line (the line orthogonal to the surface) for the surface…

A:

Q: Find parametric equations for the line pass- ing through the point P(2, –1, 4) and parallel to the…

A: Given, The line is passing through the point  P 2, -1, 4  and parallel to the vector 1, 4, -2. We…

Q: Suppose ƒ(1, 2) = 4, ƒx(1, 2) = 5, and ƒy(1, 2) = -3. Find an equation of the plane tangent to the…

A: Equation of the plane tangent to the surface  z=f(x, y) at (a, b) is z=fa, b+fxa, b(x-a)+fya, b(y-b)

Q: Find an equation of a generating curve given the equation of its surface of revolution. x2 + y2 − 2z…

A: Given equation of surface of revolution is, x2+y2-2z=0

Q: 6. For a plane with a normal of ñ = [1,2,-9] and containing a point P (3,-4, 0), write the scalar…

A: Given: Normal of the plane π is given by, n→=i→ + 2j→-9k→ Point P on the plane is P3,-4,0 To find…

Q: Consider the level surface defined by the equation x² + 2y²-32² - xyz = 8, find the following: a)…

A: Given problem:- Consider the level surface defined by the equation x2 + 2y2 - 3z2 - xyz = 8  Find:-…

Q: Find equations of the Normal plane and Osculating plane of the curve x = 2 sin 3t , y = 2t, z =…

A: Given that x=2 sin3t , y=2t and z=-2cos3t and point 0,π,-2 find equations of the normal and…

Q: Find the point-normal form equation of the plane containing the point (1, -3, 5) and the line with…

A: Solution: P(1 , -3 , 5) (2 - x ) = (y+1)/2 = -z/3 = t

Q: Find the normal vector to the surface z = xe™Y at the point (2,0, 2).

A:

Q: Find parametric equations for the normal line to the surface x² + 9xyz + y² = 11z² at the point (1,…

A:

Q: 7. Find the distance between the point (- 3, 2, 1) and the plane with equation x - 2y + 3z = 5

A:

Q: Solve for an equation of tangent plane and parametric and symmetric equations of normal line to the…

A: Given Surface is xz + 2xy + yz = 10

Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: Find the distance between the given point and the given plane. Point: (−1, 4, −2) Plane: x+2y+z=3

A: We can use distance formula to calculate the distance.

Q: Find the general form of the equation of the plane with the given characteristics. Passes through…

A: The plane, let P1, whose equation is required is perpendicular to the plane, And passes through the…

Q: Find parametric equations for the normal line to the surface x2 + 9xyz + y² = 11z2 at the point (1,…

A: Given:- x2+9xyz+y2 =11z2  To find:- Equation of normal line to the given surface at point (1,1,1)

Q: The normal vector to the tangent plane for the surface x²y³ z = 8, at the point (-1, 2, 1) is: 2 3…

A:

Q: Find the equation of the normal line to the paraboloid z = 2x² +y² at the point (1,2,6). Select one:…

A: Equation of paraboloid  To find: The equation of normal at a point P = (1,2,6).

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 distance between the point (0,0, 8) and the plane given by 2x – y + 2z – 1 = 0.

A:

Q: 7. Find symmetric equations of the line that is normal to the plane x-3y+2z=12 at the point where…

A: On the z axis a point is of the form (0,0,z). So we plug the point in the given plane to find z.

Q: Find a set of symmetric equations for the normal line to the surface xyz = 12 at the point (2, −2,…

A: The normal line to the surface xyz = 12 at the point (2, −2, −3).

Q: 3 Find the Minimum distance from the origin to the plane X+2y-z=5

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

A: Given v1 = (1 , 5 , 1)v2 = (1 , 4 , 2) Let xyz be a point in spanv1 , v2 , so there exist m , n…

Q: Give the general equation of the plane satisfying the given condition. plane Σ containing the point…

A: We will find the equation of the plane Σ which is parallel to the plain 2x − 6y + 3z = 0 and…

Q: 2-The distance between the point (2,3,1) and the plane 5x – 2y – 4z = 0 А- 0, В- 6.7, C- V45. is

A: Here, the distance between the given plane and point is zero. Because, the point is on the plane.

Q: 5. Calculate the distance between the point (3, 1, -2) and the plane 2x + y-2+1. O 10 o -10 V14 O 10…

A: The equation of the plane is  2x+y-z+1 = 0 The point is x0,y0,z0 =3,1,-2 To evaluate : The distance…

Q: Find an equation of a generating curve given the equation of its surface of revolution. 8x2 + y2 +…

A: It is required to find the equation of generating curve given the equation of its surface of…

Q: 1 8 - Find an equation of the plane containing the Point P (2,1, -1) and having the normal vutor N :…

A:

Q: The normal vector to the tangent plane for the surface xy² z³ 2 3 = -4, at the point (1, 2, -1) is:…

A:

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

A:

Q: Find equations of the Normal plane and Osculating plane of the y = 2t , curve x = 2 sin 3t , z =…

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: 1. Calculate the distance from the point P(9,4, 3) to the line which contains points A(1, 0, 1) and…

A:

Q: Find the minimum distance from the point (0,0,0) to the plane 9x+4y+z=5.

A:

Q: 4. Determine the equation of the plane passing through the point (1, –4, 3) and parallel to x – y…

A:

Q: Find parametric equations for the normal line to the surface -10x + 5y + 9z =3 at the point (1, -…

A:

Q: Find the general equation of the plane passing through P(−1, 3, −2) and having n = (−2, 1, −1) as a…

A:

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: 4. Determine the equation of the plane passing through the point (1, -4, 3) and parallel to the…

A: We have to find an equation of the plane passing through the point (1, -4, 3) and parallel to the…

Q: Find the equation of the plane tangent to and the line (in symmetric form) normal to the ellipsoid…

A: Given:   x2+ 4y2 +8z2 = 48 Point : ( -2 , 3 , -1)

Q: Find the equations of the tanget plane and normal line to the graph of In(z2) x -= 3y³ – Vx at the…

A: Given graph is                                                        lnz2x-eyx=3y3-x Again…

Q: Find all equations of normal line at the point (1, 1, –1) to the surface 2 +z² +3 = 2y + y?…

A:

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.