Calculate the distance from the point S( 3,7,-4) to the plane 6x – 3y + 2z = 0 %3D Ans d=3

Q: Find the tangent plane to the equation z = 6e* – 2y at the point (4,8,6) - II

A:

Q: Find parametric equations of the normal line to the surface z = 4 +y? at the point (2, 3, 10) O x =…

A: To Find:  the parametric equations of the normal line to the surface  z = x24+y2 at the point ( 2,…

Q: Find a point on the ellipsoid x + 3y² + z = 8 where the tangent plane is perpendicular to the line…

A: Introduction: The perpendicular vector to a 3D object f ( x, y, z ) can be calculated by computing…

Q: Find an equation of the plane tangent to the graph of g(r, y) = 3ev²-z² at the point where (x, y) =…

A:

Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 2 + 6t, z = 2t,…

A: The distance from a point P(x1,y1,z1) to a plane  is

Q: Find a vector tangent to the curve of intersection of the surfaces given by x² + y² + z² = 1 and 2²…

A:

Q: Find the distance between the skew lines with parametric equations x 2 + t, y = 1 + 6t, z = 2t, and…

A:

Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — 3ху —у? -2…

A:

Q: Find the points on the surface ( y + z)^2 + (z - x)^2 = 16 where the normal line is parallel to the…

A:

Q: Find the angle between the planes 3x – 2y + z + 4 = 0 and x + 4y – 3z – 3 = 0. Express your answers…

A: The angle between two planes is equal to the angle between their normals.

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

A: Consider the equation of a plane as, ax-x0+by-y0+cz-z0=0 Here, a, b, c, are the slopes in x, y, z,…

Q: Find the center of mass and the moment of inertia about the y-axis of a thin plate bounded by the…

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: integrate ƒ over the given region. ƒ(u, y) = y - sqrt(u) over the triangular region cut from the…

A:

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

A:

Q: Find the symmetric equations for the normal line LN to the surface S:f (x, y) = 5Vx2 + y? at the…

A: if  f is  function of (x,y,z) then gradient of f is defined asfx i + fy j + fz k ∇f is the normal to…

Q: Find the equation of the tangent plane to the surface y = 2x2 – z2 at the point (0, –1, –1) y+ 4z =…

A: We have to find

Q: Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral %3D Q…

A: The line joining P1,0 and Q0,1 is     x-11-0=y-00-1=t(say)⇒x=t+1,y=-t⇒dx=dt,dy=-dt

Q: Find the equation of the tangent plane to the paraboloid z = 2x2 +y? at the point (1,2,6). Select…

A:

Q: Find the minimum distance between origin and the plane 3x + 2y+z=14 O a. 2y2 O b. 3/2 O C. V14 O d.…

A:

Q: Find the acute angle between the planes 3x + y + z = 0 and x − 2y + z

A:

Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).

A:

Q: Find the equation on the plane tangent to the following surfaces at a given point: z=exy; (2,0,1)…

A: The equation on the plane tangent to the surface z = f(x, y) at a given point (a, b, c) is given by:…

Q: Find the tangent plane to the equation z = 3e²²-2y at the point (4, 8, 3)

A:

Q: 3. z = (c

A:

Q: Find the tangent plane to the equation z 5a2 - 4y +5y at the point (5, 5, - 200)

A: The equation of the tangent plane to a surface  is given by fx(x-a)+fy(y-b)+fz(z-c)=0where (a,b,c) =…

Q: Find a parametrization for the line through the point (a, b) having slope m.

A: Given that slope = m , this can be written as <1,m> vector. And point= (a,b)

Q: Find the distance between the skew lines with parametric equations  x = 1 + t, y = 3 + 6t, z = 2t,…

A:

Q: Find the tangent plane to the equation z 5z° + 4y – y at the point (4, 2, – 66)

A: Given: z=-5x2+4y2-y      4,2,-66

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

A:

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = 4x2 + y2,…

A: It is given that, z = 4x2 + y2, at the point (1, 1, 5) We have to find the equation of tangent…

Q: At what point on the curve x = t³, y = 6t, z = t4 is the normal plane parallel to the plane 6x + 12y…

A:

Q: Find the distance between the planes 4x + 5y + z = 25 and 4x + 5Y + z = 53. %3D

A: Explanation of the solution is given below....

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

A: Consider M is the mass of the triangular plate bounded by the y-axis and both the lines. To find…

Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. 2z…

A:

Q: Find the equation of tangent plane to the surface x² + 2y? + 3z2 = 21 which is parallel to the plane…

A: Topic- equation of tangent to surface

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

A:

Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

A:

Q: Find the equations of the tangent plane and normal line to the surface with equation 9y? + 9z2 = 22…

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 of the tangent plane to the surface z = 24 3z+4y at the point (4,3, 1).

A: Use equation of tangent plane

Q: Find the tangent plane to the equation z 4e- 4y at the point (8, 16, 4)

A: Let x0,y0,z0=8,16,4 be a point on the given surface. Then, the equation of tangent is…

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

A:

Q: 3. Find the equation of the plane tangent to xyz + x² – 2y² +z' =14 at (5,–2,3)

A:

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

A: Given vector rt=2sin3t,2t,-2cos3t. Then r't=6cos3t,2,6sin3t. The given point is 0,π,-2. Now 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 all points on the ellipsoid 2r² + 3y² + 4z² = 9 at which the plane tangent to the ellipsoid is…

A:

Q: Use t = y to parametrize the part of the line of intersection of the two planes y = 2x – 4 and z =…

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 equation of the tangent plane to the surface y = 2x2 (0, –1, 2) z at the point O y+ 4z = 7…

A: