Find all ponts on the X-XIS nat asx 4 units Prom the, MIdpoint e the line segment joiningcCoiz) and (-e-8) 12.4 units, (6,?) {(-ler8 + Yz M = (0,-3) D=(x,D) M= (0, -3) %3D units %3D %3D -x=-a=4 units %3D 25 J=525 メ=D±5

Q: 6. Find the shortest distance from B6,0,0) to the pane Ax + By tCz +D= 0 where A, B,C and D SR .

A:

Q: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x +…

A: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x + y…

Q: Find a parameterization for the line segment joining points (0,3) and (12,0) using the angle 0 in…

A:

Q: Find the distance from point P(1,1,1) to the pl r +y +z = 1

A: We have to solve

Q: An angle with its vertex at the origin of an xy-coordinate plane and with initial side on the…

A: We know, An angle with its vertex at the origin of an x-y-coordinate plane and with initial side on…

Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

A: Let ax+by+cz+d=0 is a plane  Then distance from the  a point (xo,yo,zo) is D= |axo +byo +czo…

Q: #4 Find y! of 3-y3+y2+5y-x²=D0.use it to find the eguation of the line that is perpendicular to the…

A:

Q: Find the plane thst passes through the equation of. the point P(6,0,-2) ¢ = 1+t, z=2 -t entains the…

A:

Q: Find the point(s) on x = 3 - y that are closest to point A = (1,0).

A: Given: Curve x=3-y2 and a point A(1,0).

Q: F - dr where F(x, y, z) = (4.25yz cos(xyz), 4.25xz cos(xyz), 4.25zy cos(ryz)) Evaluate п 1 and Cis…

A:

Q: Find the distance from the point (-4, 5, 1) to the plane – kr – ly – 2 = 5.

A:

Q: Evaluate F- dr where F(, y, z) = (1.5yz cos(ryz), 1.5xzcos(ryz), 1.5xy cos(ryz)) and C (*) is the…

A: We need to evaluate the line integral between the two points.

Q: Use Lagrange multipliers to find the minimum distance from the plane x+y+z=5  to the point (5,4,4) .…

A:

Q: 1. Point K is located at (4. 2, 0. 3)and point Lis located at (5. 8, -0.6). What is the location of…

A:

Q: Find the distance between the planes 3x-y+6z=7 and -6x+2y-12z=1. Round off answer to four decimal…

A: Given: To explain the correct option of the given statement as follows, The given planes are 3x-y+6z…

Q: What is the shortest distance from the point (4,0, 5) to the sphere (x – 1)2 + (y + 2)2 + z² = 36?…

A:

Q: Find the shortest distance from the point P(2,-1, 1) to the plane with =quation x - y + 2z = –1 and…

A: Shortest point of the given plane and point P.  Distance from the point P and Q

Q: (2) The distance from the point (1, 2, -1) to the plane 3x - y + 2z = 6 is. (3) Consider the…

A:

Q: find the distance from the point to the plane. (1, 0, -1), -4x + y + z = 4

A: Concept -Let the equation of plane be -Ax+By+Cz+D = 0And the coordinates of a point be - (x1, y1,…

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

A: This is a problem related to geometry part. Based on the concept of plane and point we will find the…

Q: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

A: Given: The plane equation is x+y-z=2and the distance from the point is 2,-1,1 To find the least…

Q: Find the point P nearest to Q = (−1, 3, −1) on the planex − 4z = 2

A:

Q: Find the distance between the given skew lines: x = 4+9t, y = 5+ 3t, z = 7- 6t x= 8 – t, y = 9, z =…

A:

Q: 24) By using Lagrange multiplier find a point in the plane x+2y+3z=13 nearest to the point (1,1,1)

A: We have to find a point in the plane x+2y+3z=13 nearest to the point 1,1,1 by using Lagrange…

Q: The area bounded by the curve y= 4x and the lines r = 7,1 = 10 and x - aris is O 4900 square units O…

A: From the given curve bounded region is shown below:       So,   I=∫x=7x=10∫y=0y=4xdydx

Q: 2 Find the points on the curve ax+ 2bxy + ay = c,ay = c, 0<a<b<c,whose distance from the origin is…

A:

Q: Ex: Find egns of the line thru the pt ( -!,), perpendicular bo the line 3x= 2y == and paralled to…

A:

Q: 3. Use LaGrange multipliers to find the point on the plane 2r - y+4z = 10 that is closest to the…

A: Use Lagrange method to find point

Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral 2|(xdx…

A:

Q: Find the distance from the point S(0,0,0) to the plane 20x+10y+5z=70 (approxmate to two decimal…

A:

Q: 1. Find the shortest distance from the point (1,0, –2) to the plane x+2y+z = 4.

A: We have to find shortest distance

Q: 22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of…

A:

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

A:

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

A: Given,             Point  (3, 1, −2)          Plane   x + 2y − 2z = 4

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

A:

Q: Find the orthogonal trajectories of the family of parabola described by the equation (y – 3) = = cx…

A:

Q: Find the distance from the point (0,8,9) to the plane – 2y + 3z = 11.

A: In this question, we will find the distance from the given point to the given plane.

Q: 7 Find the Paametric equ. for the line f intersect of the Planes 3x- 6y -2z =15 and 2X+Y-22%3D5?…

A: Given two lines, 3x-6y-2z=15 ....(i) and 2x+y-2z=5....(ii) Putting z=0 in (i) and (ii) we get,…

Q: 6) 3 =x2 porobola, find the yolume of the object by notating +his porabola ond the regjen around the…

A:

Q: Find a curve through the point (1, 9 whose length on the interval [1, 2] is given by i VI+ 25z!0dz-…

A: Explanation: Given a curve, ∫121+25x10dx Function f(x) has an arc length on the interval [a,b] is…

Q: to Rind the points Lagrange multiplier surface (x-1)(y-2)(Z-)=| near est Qz use on the to the point…

A:

Q: 12. Use Lagrange multipliers to find the point(s) on the intersection of the sphere r²+y²+z² = 16…

A:

Q: 27 hPlans that pas Ses through the Point C60,27 and contains the like メt4-2t)ソ= 34st) Zzス+4t 7.

A: Recall: General equation of a plane :     An equation for the plane through (x0, y0,z0 ) and…

Q: Determine the location of a point (x, y, z) that satisfies the condition(s). xy &gt; 0, z = −3

A: Here Our Aim is to determine the location of a point (x,y,z) that satisfiesthe condition(s):→…

Q: The area bounded by the curve y = 10z and the lines z = 9,7 = 11 and a – azis is O 1010 square units…

A:

Q: Find the shortest distance from the point (1, 0, −9) to the plane x + 2y + z = 9.

A: Given plane isx + 2y + z = 9and point (1, 0, -9)We have to find shortest distance

Q: Find the distance between the planes  5x − 3y + z = 5  and  5x − 3y + z = −9.

A: Two planes  and will always be parallel if The given planes  and  are parallel because we can see…