Ex 6/ Find the Velume in the firstad Lacdlesiged by the Cylinder xpZ54 and the plane ye 3 22

Q: ax + by + cz + d, = 0 13) Show that the distance between the parallel planes: and ax + by + cz + dz…

A: here we have to prove the formula of distance between 2 parallel planes.

Q: The coordinate axes divide the xy-plane into four sectionscalled________?

A: The coordinate plane looks as below:

Q: Find two different planes whose intersection is the line x = 1 + t, y = 2 - t, z = 3 + 2t. Write…

A: Given:

Q: Find the distance, d, between the point S(4,8,4) and the plane 8x + 7y + 3z = 40. The distance, d,…

A: Given:       Point =S4,8,4        Plane 8x+7y+3z=40                  8x+7y+3z-40=0 Distance between…

Q: Find the length of the curve 36y2 = (x — 4)3 , 2 ≤ y ≤ 3, y ≥ 0.

A:

Q: Sketch the surfaces 1. 9x2 + y2 + z2 = 9  2. 4x2 + 9y2 + 4z2 = 36

A: Using graphing calculator to graph them. 9x^2 + y^2 + z^2 = 9

Q: Find the distance between the parallel planes – 2x + y + z = 0 and бх — Зу — 32 -13 — 0. %3D

A:

Q: Ex 3 identify the equarion of a line a) parallei that is é b) perpendicular y= x-2 through ly,-1)

A:

Q: Which of the following is the total length of the curve of intersection of the surfaces x2 + y? + 22…

A:

Q: Calculate the distance from point s(10, -8, 10) to the plane 2x + 2y + z = 4 O 10 O 10 의 ~m 의 29

A: Given query is to find the distance between the plane and point. The given point is S(10, -8, 10)…

Q: 1. Find the distance from the point S(2,-3,4) to the plane x+2y+ 2z =13

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

Q: The smaller angle (in degrees) between the planes x + y + z =1 and 2x - y + 2z = 0 is

A: Introduction :

Q: Show that the distance between the parallel planes                                          ax + by…

A:

Q: Find two different planes whose intersection is the line x = 1 + t, y = 2 – t, z = 3 + 2t. Write…

A:

Q: Find the acute angle (in degrees) between the planes Sz + 3y +5z 1 and 2z

A: P1 denotes plane 1 P2 denotes plane 2

Q: The distance from (4,-5, 10) to yZ-plane is O A.4 O B. 5 C. /141 OD.10 OE. 125

A: Solution is given below:

Q: Q: To find an angle between planes 2x + 4y - 4z- 6 = 0 and 4x + 3 y+9=0.

A: We have to find the angle between the given two planes.

Q: Eliminate the parameter from x = 2sint, y=4cost

A:

Q: Find the distance between the parallel planes 2x +y + z = 0 and - 6x – 3y-3z – 13 = 0. | NOTE: Enter…

A:

Q: Find the distance between the parallel planes – 2x + y + z = 0 and 6х — Зу — 3г — 22 — 0. - NOTE:…

A: Find the distance between the parallel planes.

Q: Find the acute angle (in degrees) between the planes – 4x – 5y + 5z = 0 and 2x – 3y + 3z = - 7.

A: As per the company's guidelines we are supposed to answer only one question.Kindly repost the other…

Q: Find the length of the curve. (2t + 1)3/2 2.y = Osts 16 x= 3

A:

Q: Find the point on the line y = 3x + 5 that is closest to the origim %3D (x, y) = %3D

A: We have to solve

Q: Find the acute angle between the planes x = 7 and x + y + sqrt(2)z =-3.

A: We know that cosine of angle between plane a1x+b1y+c1z=d1 and a2x+b2y+c2z=d2 is given by

Q: Sketch the section of the surface at y= 0. 4. + 9 36

A: Given the equation4x2+9z2=36

Q: Tind he latance from the pomt (-2, 4) to tu plane 37+2y4 6E5

A: Given a point (1, -2, 4) and a plane 3x + 2y + 6z = 5

Q: Find maxi mal reete of change of a functron flx,y)=xy²+Vz a poiet (R,4).

A:

Q: 8. Find the angles between the planes r+y = 1, 2x+ y – 2z = 2

A:

Q: find the engle of intersection between 2x - 4y + 4z = 7 and 6x + 2y – 3z = 2 .

A: Consider the given planes: 2x-4y+4z=7So,n1→=2,-4,46x+2y-3z=2So,n2→=6,2,-3

Q: Find the distance from the point S(5, -9,6) to the plane 2x+ 10y + 11z = -10 4. O A. 225 52 B. 5 4…

A: Given:  S(5,-9,6)  And equation of plane is  2x+10y+11z+10=0

Q: Sketch the surfaces ASSORTED 16x2 + 4y2 = 1

A: we have to sketch the the surface 16x2+4y2=1

Q: Find the length of the curve. 2,3/2,0 st s9 x= 4t, y 3 61 242 2 3 O 2. seçenek 4. seçenek 122 61 3 3…

A: We can find the arc length as below

Q: Find the acute angle (in degrees) between the planes - 2x – 5y + 2z = 0 and 2x + 3y – 2z = 5. :-2 0…

A: The given equation in the vector form is, a=-2x-5y+2zb=2x+3y-2x Then, a=-22+-52+22=33b=22+32+-22=17…

Q: Find the acute angle between the planes x = 7 and x + y + √2z = -3.

A: Acute angle between two planes a1x+b1y+c1z+d1=0 and a2x+b2y+c2z+d2=0 is,…

Q: Find the distance (d) from the paint (9, 4, 6) to the plane z-y = 5. STAAVE

A:

Q: Find a parametrization for the line segment beginning at P, (-5, - 2,3) and ending at P2 0, 5/4

A: We have to use parameterization of the line.

Q: 2.5 What is the distance between two parallel hyperplanes {r E R" | a"x = b1} and {r E R" | a"x =…

A:

Q: Find the cylinder surface determined by Curve 4x?+9g? -36=0 and d= ( 1, -1. 32 line.

A:

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: find the surface of both of the trainagles, all the sides *show all the work*

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

Q: Evaluate 2-1 dz where C is contour defined by lz-3il: 113

A:

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

A: The given equation of plane is 3x+4y-5=0 and the point is P0=3, 9, 6. The distance between a point…

Q: Find the acute angle (in degrees) between the planes 5x + y + 4z = O and a y + 2z = – 3.

A:

Q: 8. Find the angles between the planes r + y = 1, 2x + y – 2z = 2

A: We will use direct formula to find the angle. The detailed solution is as follows below:

Q: Ex (50) / Find the distance from the line = 2 +t, y = 1 +t, z = -1- 2t to the plane x + 2y + 6z = 10

A: Using. Distance formula form line to plane,

Q: The distance from (10,-9,5) to yZ-plane is - 10 B.9 OC.5 OD. 206 OE. /106

A: We will find the distance between the point and the yz plane as following.

Q: Show that line y+1 is parallel to plane x- 2y + z = 6 С.

A:

Q: Evaluate the length of the curve y = 2 + Vx , 3 < y< 4

A:

Q: Identify the length of the curve 1X = ²+2y — In(y + 1), for 0 ≤ y ≤ 2. - 8

A:

Q: Find the distance, d, between the point S(9,3,5) and the plane 9x + 1y + 1z= 36. The distance, d,…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.