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

Q: Find parametrizations for the lines in which the planes 5x - 2y = 11, 4y - 5z = -17

A: Given: The given two planes  5x-2y=11 and 4y-5z = -17 are intersects.

Q: Find the points on the surface 1x? + 3y2 + 5z2 = 1 at which the tangent plane is parallel to the…

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 a parametrization for the curve. the line segment with endpoints (-1, 3) and (3, -2)

A:

Q: Find the distance between the point and the plane. 19. (0,0,0) and 2x+3y+z12 20. (2,8,4) and 2x+…

A: a) given point is (0,0,0)  plane is 2x+3y+z=12 find the distance between the point and the plane  b)…

Q: find a parametrization of the curve. The line passing through (1, 0, 4) and (4, 1, 2)

A: Given: A line is passing through the points 1, 0, 4 and 4, 1, 2.

Q: Find a parametrization for the curve described below. the line segment with endpoints (4,4) and…

A: Given,  A line segment with endpoints 4, 4  and  6, 1  We have to find the parametrization of the…

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 the distance between the point and the plane.

A: The distance of a point from a plane in the standard equation form is equal to . The given point…

Q: Find a parametrization for the line segment beginning at P1 and ending at P2. 25) P1(-4, –5, 4) and…

A:

Q: findthe parametríc equatlons for the line through the paint of in tersecti of the lines 4=X=2+ 36 14…

A: first we find intersection point of given line

Q: Find a parametrization of the line through P = (4, 9, 8) perpendicular to the yz-plane.

A: Equation of Linethe Line through P =(x0,y0,z0) in the diresction of vector v→=(a,b,c)is defined…

Q: Find the point(s) on the plane 4x +3y +z = 2 that are closest to (1,-1,1).

A:

Q: Find parametrizations The portion of the plane 4x + 2y + 4z = 12 that lies above the square 0<=…

A:

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: Give two different parametrizations of the line through (4, 1) withslope 2.

A: Solution:GivenA point(4,1) with slope 2Formula:Equation of the line at (x1,y1)y-y1=m(x-x1)

Q: Find parametrizations for the line in which the planes 3r - 6y-2z = 3, and 2x+y-2z = 2 intersect.

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: Use Eq. (8) to find the distance from Q = (1, 1, 1) to the plane2x + y + 5z = 2.

A: Find the distance from Q=(1, 1, 1) to the plane 2x+y+5z=2 or 2x+y+5z-2=0.…

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

A:

Q: Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?

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 Parametrization of the line.

A:

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

A:

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

A:

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 a parametrization for the line segment beginning at P, (-5, - 2,3) and ending at P2 0, 5/4

A: We have to use parameterization of the line.

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: Which of these describes a parametrized line perpendicular to the plane 3x + 2y + z = 15? A) (2 +…

A: The direction ratio of the normal vector to the plane is (3, 2,1 ) So the perpendicular line to the…

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

A:

Q: parametrization for the line segment beginning at P1 and ending at P2. P 1(-4, 0, 3) and P 2(0, 5,…

A:

Q: Find parametrizations for the line in which the planes 3r- 6y – 2z = 3, and 2x+y-2z = 2 intersect.

A: Given Equation of planes 3x-6y-2z=3 and 2x+y-2z=2

Q: Which of these describes a parametrized line perpendicular to the plane 3x + 2y + z = 15? a)…

A: The direction ratio of the normal vector to the plane is (3, 2, 1) So the direction ratio of the…

Q: find the (dis tan ant) between the planes ml and m2 when ml =: 3x - 2y+z = 9 and m2 =: 6x - 4y+ 2z =…

A: Consider the equation of planes m1: A1x+B1y+C1z+D1=0  m2: A2x+B2y+C2z+D2=0Two planes are parallel if…

Q: find the distance from the point to the plane. (3, 0, 10), 2x + 3y + z = 2

A: the given point is (3,0,10) the given equation of the plane is 2x+3y+z=2 we have to find the…

Q: Find a parametrization for the line segment beginning at P1 and ending at P2. P 1(7, 2, 4) and P…

A:

Q: Find a parametrization for the line segment beginning at P, and ending at P2. P (2,-3,2) and P2(0, –…

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: Flnd the parametric equation of the line of ntersection of the planes and

A: First find normal vector then take cross product and use formula

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

A:

Q: Find the equation of the line tangent to the intersection of the surface z = arctan ry with the…

A: The tangent line to a plane curve at a particular position is the straight line that "just touches"…

Q: Find the distance from the point B = (1,0, 2) to the plane 2P whose general equation isx + y - z =…

A: Given: equation of plane is x+y-z=1  We know that distanced from the pointx1,y1,z1 to the…

Q: Find the parametric equations for the line of the intersection L of the two planes. 6x – 3y+ z = 5…

A: Parametric equations of the line is :  x(t) = x0 + a t  y(t) = y0 + b t  z(t) = z0 + c t  Here ( x0…

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

A: Plane