Find the point (if it exists) at which the following plane and line intersect. y = - 10; r(t) = (4t + 2, – t+ 4,t – 6), for - o

Q: Find a plane containing the point (6,-7,7) and the line x(t) y(t) z(t) = = = - 2 - 6t - 1 + 5t 5-t

A: Here we have to find the equation of plane

Q: Find a plane containing the point (7,3,5) and the line x(t) - 3 + t | y(t) 8 +t z(t) - 3 + 5t

A:

Q: Q1// A :- Find an equation of the plane that passes through point (1,4,3) and contains the line…

A:

Q: Find the point on the plane x+5y+2z=14 closest to the point​ (1,1,1).

A:

Q: Suppose f(x, y, z) = In(7x + 9y+7z). Find an equation for the level surface of f that passes through…

A: Given Data: The level of the curve for fx,y,z=In 7x2+9y+7z2 is of the form,…

Q: Find the point​ (if it​ exists) at which the following plane and curve intersect.   z=13​; r​(t)=t,…

A:

Q: H.W: Find the point where the line x=+ 2t , y=-2t intersects the plane 3x+ 2y +6z 6 z= 1+t

A:

Q: Q4. Find an equation of a plane that contains the line x=t, y=1+2t, z=2-t.

A: We have to find the equation of plane .       According to our guidelines ,we cannot solve all…

Q: Find the point at which the line x(t) y(t) z(t) - 5+ 5t -6-8t intersects the z plane. - 7+8t

A:

Q: 3. Find the general form of the equation of the plane containing the point Q(0, -2, 10) and the line…

A:

Q: Find the point in the plane x – 2y + z = 4 that is closest to the origin.

A: Solution)                   Given                           plane  x-2y+z =4

Q: Find an equation of the plane containing the lines L1 and L2 in R3 L1: x = t ; y = -t ; z = t L2:…

A: We have to find equation of plane containg Line L1 and L2  -

Q: Find the points on the surface x² + y² + z² = 4 farthest from the point (1,–1,1), 2 %D

A:

Q: Find the point P where the line x = 1 +  t,  y  =  2t,  z = - 3t  intersects the plane x + y - z =…

A: Given line: x=1+t,  y=2t,  z=- 3t

Q: Q8) The distance between the line x=-1+t, y=3+2t, z=-t and the plane :2x-2y-2z=3 is

A:

Q: Find a plane containing the point (5,-6,-3) and the line x(t) y(t) z(t) = = = - 4 - 7t 1 -8t 3 - 4t

A:

Q: Find the point P where the line x = 1+t, y= 2t, z= -3t intersects the plane x+ y -z = -3

A:

Q: Q8) The distance between the line x=-1+t, y3D3+2t, z=-t and the plane 2x-2y-2z=3 is: *

A:

Q: Find all planes in R^3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

A: To find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.…

Q: Find a plane containing the point (-3,3,-3) and the line F(t) = +t

A:

Q: Q4:Show if the line (x = 5y +17, y+z-2= 0) lies in the plane 3x-41y-26z +1 = 0 or no ? Where does…

A:

Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: Use equation of plane

Q: Find an equation of the plane containing the point (3,0,-4) and perpendicular to the line r(t D)= O…

A:

Q: O Find an equation for the plane through the point P = (3, −2, 4) that is perpendicular to the line…

A: Given problem:- Find an equation for the plane through the point P = (3, -2, 4) that is…

Q: Find the equation of a plane through the point(- 3, – 2, 3) and orthogonal to the line x(t) - 5+ 8t…

A:

Q: H.W: Find the point where the line 8 x=+ 2t , y= -2t , = 1+t intersects the plane 3x + 2y +6z = 6

A: Given that:                    The line with equation:      x=83+2t, y=-2t, z=1+t     & Plane:…

Q: The line L(t) = (4 – 3t, 3, 1 +t) intersects the plane 3x – 3y + 2z = -16 at the point when t =

A: To find the point of intersection of the line and the plane, substitute the values of x,y, z from…

Q: Q5: Find the distance of the point (2. –2,1) from the line x-2 y-3 z+2 %D 2 4 3 measured parallel to…

A:

Q: 2. Assume that the plane P3 is perpendicular to the yz-plane, and the line l2 : x = 2t, y = t, z =…

A:

Q: H.W: Find the point where the line y=-2t, 1+t intersects the plane 3x+2y +6z 6

A:

Q: Q:- find the line of interseetion o f the given by 3X +6y -SZ=-3 S the plane plane -2x + 7y -Z=24 1)…

A: We know that a straight line is the intersection of two planes. So a pair of equations of first…

Q: Find the number  a such that the line x = a  bisects thearea under the curve  y = 1 / x 2  , 1<…

A: Our Aim is to find a number such that line x=a bisects the area under the curve y=1x2, 1≤x≤4.

Q: Find the point at which the line r(t) y(t) z(t) = -6-7t 7+t - 54t intersects the z plane.

A: Let's find intersect points.

Q: 3. Find the equation of the plane containing both the point (1, 2, 3) and the line r(t) = (t, 2t+1,…

A:

Q: Find the point at which the line 7(t) = +t intersects the yz plane.

A:

Q: y. Find the exact coordinates of the point of intersection of the line x+2 = 3 and the plane 3. 2x -…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: (b) Find the points on the line r(t) = (t, 1+2t, 1-2t) whose distance from the plane 2x - 2y+z=1 is…

A:

Q: Find the point on the graph of z = x2 + y2 + 10 nearest the plane x + 2y - z = 0.

A:

Q: A. Find an equation of the level surface of f(r, y, 2) = 4.x2 + 22 that passes through the point…

A: Given:     f(x,y,z) = 4x2 + z2      Point: ( 1 , 2 , 3 )

Q: Q3: Let L: x-2+3t, y 2t-1, z-4t and M: x+2y+z-11, and let (p) be thus point of intersection. Find…

A: given line is                                                         L1: x=2+3t, y=2t-1, z=4tM:…

Q: Find the point at which the line y(t) z(t) = 2 + 4t -6-8t intersects the yz plane. 6-7t

A: The line x(t)=2+4t, y(t)=-6-8t, z(t)=6-7t intersect yz plane Note:    Multiple questions are given,…

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Equidistant points mean that the distance of two points represented by P1 and P2 is equal to the…

Q: Find the point at which the line 7(t) +t intersects the | xz plane.

A:

Q: -:Q1 Evaluate , (x- 2y) dA, where R is the parallelogram in the xy-plane with vertices (0,0), (4,1),…

A: The objective is to evaluate ∫∫Rx-2ydA where R is the parallelogram in the xy plane with vertices…

Q: H.W 8- Find equations of the planes that are parallel to the plane x +2y- 2z= 1 and two units away…

A: