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

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

A:

Q: Find the equation of the plane in the form z=c+mx+ny containing the line in the xy-plane where x=3,…

A:

Q: find the intersection point between the line      X=1+2t {    y=2-t       Z=3 and the x+y-z=3…

A: The intersection point will be common to both the line and the plane. Therefore, substitute the…

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

A: Given : The equation of the planes are x+ 2y + 6z = 1 and x + 2y + 6z = 10 .

Q: Find the distance from the origin to the plane 2 = z - x.

A: Given point is (0,0,0) Given plane is 2=z-x or x-z+2=0

Q: Find the standard equation of the sphere with center (−3, 2, 4) that is tangent to the plane given…

A: Radius (r) will be the distance from the center to the tangent plane. That is the distance between…

Q: Find an equation for the set of points equidistant from the xy-plane and the yz-plane.

A: Find an equation for the set of points equidistant from the xy-plane and the yz-plane.

Q: Find the equation for the tangent plane to the surface Z =-8x² - 3y2 at the point (2 1, -35). O 2x +…

A: We can find the answer as below

Q: Let P be the plane that is tangent to the equation xyz + 260 = z' + 30x + 26y at the point (7,7,4)…

A: The tangent plane to the surface is a plane that only touch the surface at the point.

Q: Find an equation of the sphere with center (2, 1,−3) that is tangent to the plane x −3y + 2z = 4.

A:

Q: 2. Find the equation of the plane tangent to the elliptic paraboloid z = point (1, 1,3). 2.a2 +y, at…

A: To find out the equation of the plane tangent to the elliptic paraboloid.

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

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

A:

Q: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

Q: Find the distance between the planes x + 3y – 2z = 3 and 2x - y - z = 4. %3D

A:

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

A:

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

A: Given a point, (2, 0, 0) and the equation of the plane x + 2y + 2z = 0.

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

A:

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

A: Given the equation of plane:

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 distance from the point (3, 4, -1) to the plane lr 3y +2z = 5.

A:

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

A:

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

A:

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

A:

Q: Find the distance between the point (0, 0, 0) and the plane 2x + 3y + z = 12.

A:

Q: Find the point on the plane 2x + 3y + z = 7 that is nearest to​ (2,0,1).

A: NOTE: Refresh your page if you can't see any equations. . the given point is . the given plane is…

Q: Find the equation of the plane tangent to the grapl UI z = f(x, y) = x² + 2y³. + 1 at the points in…

A:

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 the distance between the point and the plane. 19. (0,0,0) and 2x+3y+z=12

A: As there are multiple questions, the first one (19) is solved here.

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

A:

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

A:

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

A:

Q: find an equation for the plane that is tangent to z=4x^2+y^2 at the point (1,1,5)

A:

Q: Find the distance between the point (3,11,-2) and the plane X t 2y

A: Explanation of the answer is as follows

Q: Find the distance between the point and the plane. (0, 0, 0) 2x + 6y + z = 12

A:

Q: Find the points on the surface 1x^2+2y^2+5z^2=1 at which the tangent plane is parallel to the plane…

A:

Q: Find an equation for the plane tangent to the surface z = 2x2 - 7y at the point (3,-1,5)

A: Given surface z=2x2-7y and the point 3,-1,5. The main objective is to find an equation for the plane…

Q: Find the distance between the plane x+y +z = 3 and the line L= λ(1,0,-1).

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: Find parametrizations for the lines in which the planes x - 2y + 4z = 2, x + y - 2z = 5

A: Given the planes :- x - 2y + 4z = 2,  x + y - 2z = 5   The Arbitrarily set z =1 and solve the…

Q: Find the distance between the point P(1, 1, 1) and the surface x² + 2y² + 3x² = 1.

A: Given Point P1, 1, 1 and surface x2+2y2+3z2=1

Q: Find the point on the plane x+y+z%3D24 that is closest to the point (1,1,1).

A:

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

A:

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…

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

A: GivenQ=0,0,0p:x−2y+2z=1

Q: Find the equation of the plane in the form z = c + mx + my containing the line in the xy-plane where…

A: Plane