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

Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (-4, 2, -44).

A: The solution is given as

Q: 33 and Complete the parametric equations for the line where the planes – 3x – 9y – 12z = - 11x + 2y…

A:

Q: - 6y Find the tangent plane to the equation z at the point (12,24,4) z =

A:

Q: Find an equation of the plane tangent to the following surface at the given point. z=6-3x- 3y; (2,3,…

A:

Q: Find the parametric equation of the line that passes through point P(2,3,4) and is perpendicular to…

A: To Determine: Find the parametric equation of the line that passes through point P(2,3,4) and is…

Q: Find an equation of the tangent plane to the surface defined by the equation zf(x, y) + 2³ = 3 at…

A: The given surface is:zf(x, y)+z3=3The point is (-1, 2, 3)

Q: Find parametric equations for the line segment joining the points (5, 3) and (11, 11). x=t, y = 3 +…

A: Solution

Q: z = In (x² + y²) at point Po(1,0, 0).

A:

Q: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x) %3D and C is the curve in the third quadrant…

A:

Q: A parametric equation of the line of the intersection of the planes x - z = 0 and x – y + 2z = 0 is

A:

Q: Find parametric equations for the line segment joining the points (6, 2) and (9, 10). x=t, y 2+8t,…

A:

Q: Identify a generating curve on the xz-plane for the surface of revolution with equation x? + y? +z?…

A:

Q: Find the equation of the tangent plane to the surface z = 4 +y? at the point (2,-3, 10) Ox+ 4y- z =…

A:

Q: Find the angle between the two planes 3x + 2y − z = 7,  x − 4y + 2z = 0 and find a set of parametric…

A: Known fact: The angle between two planes a1x+b1y+c1z+d1=0  and a2x+b2y+c2z+d2=0 is given by…

Q: z = In(x²y*) + / x² + y²

A:

Q: Find an equation of the plane tangent to the following surface at the given point. z = 6 - 4x2 - y2;…

A: By using equation of tangent plane for surface, we calculate the required tangent plane.

Q: Find the equation of the plane tangent to the surface of Z= x2+ Y2 at point P(125)

A:

Q: Find the (perpendicular) distance from the line given by the parametric equations æ(t) 3 – 4t %3D…

A:

Q: Find the equation for the tangent plane to the surface z=-8x2 -4y2  at the point   (2,1,-36)

A:

Q: Find the length of the parametric y = 2 , - V3sts V3. curve x = 1+

A:

Q: Complete the parametric equations for the line where the planes – 8z – 2y – 5z = 0 and - 4x + 2y –…

A: Given: The planes are -8x-2y-5z=0 and -4x+2y-9z=0 To find the parametric equation xt, yt, zt

Q: s) Find the parametric equations of the line that is perpendicular to the plane 2x +y+3z = 4 through…

A:

Q: Find the angle between the two planes x- 2y + z = 29, 2x + 3y – 2z = 6. And also find the parametric…

A: here we will find angle between two planes and parametric equation of plane's line of intersection,

Q: Complete the parametric equations for the line where the planes 8x + 11y + 4z 13x + 2y + 3z = 5…

A: This question can be solved using the concept of lines and planes in three dimensional geometry.

Q: Find the parametric equation for the line where the planes 4x – by + 8z = - 36 and – by + z = – 15…

A:

Q: At which point will the plane 2x + 4y – 3z = -48 and the line given by the parametric equations x =…

A:

Q: Find an equation of the line through (0,0,0) that is parallel to the e parametric equations x(t) = 2…

A: To find out equation of any line we need one point on the line and a vector which is parallel to the…

Q: Find the parametric equation of the line of intersection of two planes correctly: P1:x+3y+5z=0 and…

A:

Q: Find the equation of the tangent plane to the surface 2 = r - 2r'y+ 2r y at the point where x = 1…

A:

Q: Find the equation of the tangent plane to the surface of the equation z = x2 + y2 - 2xy on the point…

A: Equation of tangent plane

Q: Find the parametric equation of the intersection of the planes x + y = 1 and x + z = 2.

A: Equation of plane 1 - x+y = 1        Normal vector of plane 1 = n1 = 1,1,0…

Q: Find parametric equations for the line in which the planes x + 2y + z = 1 and x - y + 2z =-8…

A: x + 2y + z = 1 and x - y + 2z =-8 are the two planes.Let z=t So, the equations become:

Q: Find the equation of the plane perpendicular to the curve r(t) = (sin(3t), 2t, – cos(2t)) %3D at the…

A:

Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + Z?…

A: Solution-

Q: Find the equation of the plane that passes through the point (2, 1, 1) and is tangent to the surface…

A: We have to find the equation of the tangent plane.

Q: Find the equation for the tangent plane to the surface z= In (7x + 10y + 1) at the point (0,0,0).

A:

Q: Find the parametric equation for the line where the planes 7x – 6y + z = 10 and 2x + y – 3z = 4…

A: We have, r(t) = (0, -2, -2) + t(17, 23, 19) The detailed solution is as follows below:

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: Compute the parametric equations of the line in R3 determined by the intersection of the two planes:…

A: To obtain the parametric equations of the intersection line, use the following formulae. Let n1→…

Q: Find the equation of the plane tangent Z= x2+ Y2 at point P (1,2,5) to the surface

A: Equation of tangent plane on the surface z=f(x,y)  at the point (a,b,c)  is given…

Q: Find the equation of the tangent plane at the point (-2,1 – 3) to the ellipsoid surface + y? + = 3.

A: Find the equations of the tangent plane and normal line at the point (-2, 1, -3) to the ellipsoid…

Q: Find the equation of the plane tangent to the surface z x+y at the point (2, 1, 3). x-1

A:

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 an equation of the tangent plane to the given surface at the specified point. z = 6x² + y² -…

A: This question is based on finding equation of plane to the given surface at a point.

Q: Find an equation of the plane tangent to the surface f(x, y) = xy² – 5x at the poin (1, 2, –1).

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: A curve in the plane is defined parametrically by the equations x = t +t and y t* + 2t2. An equation…

A: The equation of the tangent line is: y-y1=mx-x1 Where m is the slope of the tangent line. And The…

Q: Find the point at which the line with parametric equations x = 3 + 4t, y = 5 – 2t, z = 4 + 7t…

A: According to question,Given equation of line in parametric form,x = 3+4t,y = 5-2t,z= 4 +7t,Equation…

Q: Sketch the plane curve r(t) = t2i + 2tk, and find its length over the given interval [0, 3]

A: We have, r(t)=t2i+2tk  we have to determine the length of the curve over the interval [0,3]

Q: Find the equation of the tangent plane and the normal line to the surface z=-2x -8y at the point…

A:

Q: Find the equation of the tangent plane to the surface z = +y? at the point (2, –2, 5)

A: