H.W: Find the distance from S (1,1,3) to the plane 3x+ 2y+ 6z = 6

Q: 20. Find the point at which the line a = 1+ 2t, y = 4t, z = 2 –t intersects the plane r+y – 2z +1=…

A: Given that, equation of line:- x=2t, y=4t, z=2-t Equation of Plane:- x+y-2z+1=0

Q: a) Find the acute angle in degree between the planes défined by 8x + 10y + 3z = 4 and 2x + 4y + 6z =…

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

Q: Q7. What angle does the line of intersection of the plane O make with the nonnegative 2x + y - z = 0…

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: Evaluate / x2 zdS, where S is the part of the plane z = 4+ 3x + y above the rectangle [0, 4] x [0,…

A:

Q: Fin He ara at tHe surface af the portion oF Hae Plane 2= 5-2X -9y

A:

Q: a) Show that the distance between the parallel planes Ax + By + Cz = D1 and Ax + By + Cz = D2 is |D1…

A: (a) To show that the distance between two parallel planes Ax+By+Cz=D1 and Ax+By+Cz=D2 is…

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

A:

Q: Find equations for the planes The plane through P0(0, 2, -1) normal to n = 3i - 2j - k

A:

Q: Find the point of intersection, if any, of the plane T: 4x + 2y – 2z=1 and the line l : 3 +t 1

A: Point of intersection of line and plane

Q: 4. Find the angle made between the two planes: r+ y - z = 5 and 2r + y +3z = -1.

A: Given that: Equation of first plane: x+y-z=5   ........(1)Equation of 2nd plane: 2x+y+3z=-1…

Q: O Find the distonce from the point pC1,\, 1) to the plane 2K-3y+72=1

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Q: Use Green's Theorem to evaluate (V1+r) dr+2ry dy, where C is the triangle with vertices (0, 0),…

A:

Q: (a) Prove that the lines with parametric equations: x = 1+t, y = 1+ 6t, z = 2t and x = 1+ 2s, y = 5…

A: aLet the L1 be the line:x=1+t, y=1+6t,z=2tand L2 be the line:x=1+2s, y=5+15s, z=-2+6sThe direction…

Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y +z = 1 that lies above the…

A:

Q: For what positive value of cc is the acute angle between the plane containing the points A(0,0,1),…

A: According to the given information, it is required to find the positive value of c is the acute…

Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

A:

Q: 3. Find the distance from P(1, 1, 1) to the plane II with equation r – 3y + 4z = 10.

A: Distance between point and plane is (4√26)/13.

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

A:

Q: Find the symmetrical point of point P(1, 3, 4) with respect to the plane D:3x-2y+z+6=0.

A: Symmetrical point at plane problem....

Q: Evaluate x* zdS, where S is the part of the plane z = 1+4x + 3y above the rectangle [0, 3] x [0, 5]

A: Please see the below picture for detailed solution.

Q: 7. Find the dis to the plane x +2y+ 6z = 10 %3D 8. Find the angles between the planes a+y= 1,…

A: According to guidelines we should have been able to solve only one question at a time #8

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: Find the distance from a point P(x1, y1, Z1) to the plane Ax + By + Cz = D.

A:

Q: Find for the point P(x,y,z) on the plane 3x + y – z – 15 = 0 that is closest to the origin.

A: The distance of the point P(x,y,z) from the origin is: d2=x2+y2+z2 Now we have to minimize d if the…

Q: x − 3y + 6z = 4 e 5x + y − z = 4

A: For the equation of plane a1x+b1y+c1z+d1=0, a2x+b2y+c2z+d2=0The angle between them is given…

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

A: tangent plane and normal line

Q: Find the distance, d, between the point S(5,6,5) and the plane 6x + 7y + 1z = 12. The distance, d,…

A: topic- distance between point and plane shortest distance of plane ax+by+cz+d from point…

Q: Let R be the triangle in the xy-plane with vertices (0,0),(0, 1),(1,0). Find C[n(2 – x – y) dA.

A: Given vertices of triangle now we have to find the area as shown below

Q: // 2° zdS, where S is the part of the plane z = 4+ 2æ + y above the rectangle [0, 5] × [0, 3]…

A:

Q: c. Find the distance from Po = (3,9, 6) to the plane 3.x + 4y – 5 = 0.

A:

Q: Find the projection of a on the plane P if a 4 and P has the equation x + y + z = 1.

A:

Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y + z = 1 that lies above the…

A: Surface integral

Q: (A) Find the Distance between the point (x.y.z) and the plane 3x+2y+6z = 6 8 If the plane meet with…

A: As per the company policy i can answer only first question for you, More than that leads me towards…

Q: H.W: Find the polnt where the line *+2t, y-2t z 1+t intersects the plane 3x+ 2y +6z 6 2.

A:

Q: a) Show that the line I = 0, y = t, z =t where te R a) lies in the plane 6z+4y–4x = 0 b) is parallel…

A: In the question it is asked to solve for the planes having equation given below.

Q: Find the cosine of the angle, 0 Ses x/2, between the plane x +2y-2z= 2 and the plane 4y-5x + 3z =…

A:

Q: Find b such that B = (0, b) has hyperbolic distance of u from the point A (0,0).

A: Given: B=(0,b) has  hyperbolic distance of u from the point A=(0,0) Formula used:

Q: 17. F = |r|r, where r = xi + yj + z k, S consists of the hemisphere z = /1 – x² – y2 and the disk x?…

A: The solution are next step

Q: 4) Find equations for the planes: a. The plane through P(0,2,-1) normal to n = 3i-2j-k

A:

Q: a) Prove that the lines with parametric equations: x = 1+ t, y = 1 + 6t, z = 2t and x = 1+ 2s, y = 5…

A: Given that: Line L1:  x=1+t, y=1+6t, z=2tLine L2:  x=1+2s, y=5+15s, z=-2+6s

Q: e|| x°zdS, where S is the part of the plane z = 1+ 4x + 2y above the rectangle [0, 4] x [0, 2]…

A:

Q: Consider the planes P and Q given as 2x-3y + z = 3 and 4x- 6y + 2z = 5: Are P and Q parallel? Find…

A: Consider the planes P and Q given as 2x-3y + z = 3 and 4x- 6y + 2z = 5: Are P and Qparallel? Find…

Q: Evaluate | x° zdS, where S is the part of the plane z = 2 + x + 4y above the rectangle S [0, 4] ×…

A: It is given that S is the part of the plane z = 2 + x + 4y above the rectangle [0, 4] * [0, 3]…

Q: 12. Find the distance from the point P(0,0,0) to the plane given by x + y +z= 6.

A:

Q: Given Fxy 2) = (z², xy, yz) and C is a triangle in the plane x + y + z = 2 with vertices (1,1,0),…

A: We will use basic knowledge of vector calculus.

Q: For what positive value of c is the acute angle between the plane containing the points A(0,0,1),…

A: Calculate the vector normal to the yz plane. Equation of yz plane:x=0Equation of vector normal to yz…

Q: 17. Find the angle between two planes below. a. 2x- y+= =5 and 3x + y-z =1 b. 2x - 4y + 6z = 1 and…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.