Find a plane containing the point (-3,3,-3) and the line F(t) = < 8, 3, 7 > +t< - 4, – 8, – 6>

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: Find the equation of the plane containing the line of intersection of the two planes z+y+z+5=0 and…

A:

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

A:

Q: 2.) Find the Symmetric form of the equation of the line of in tersection of the two Planes X-Y +Z…

A: Let a, b and c be the direction ratios of the required line. Since the required line lies in both…

Q: Find a function r(t) that describes the line through P(3,4,5) that is orthogonal to the plane 2x-z=4

A:

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

A:

Q: Find a plane containing the point (7,-8,8) and the line F(t) = +t

A: Given that, the point is 7,-8,8 and the line is r→t=-6,-8,-7+t6,8,4. From the given line, the point…

Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0,1,1).

A: First we find out normal vector to the given plane than find out the point that is closed to the…

Q: Find an equation of the plane that contains the point P(5,0,2) and the line x = 3t +1, y=-2t + 4, z…

A:

Q: Find the point on the plane x + 2y + 3z = 13 closest to the point (1, 1, 1).

A: Given plane is We need to find the point on the plane closest to

Q: Find an equation of the plane through the point (2, 0, 1) and perpendicular to the line x = 3t, y =…

A:

Q: Let L be a line which passes through the point (-5,0, 1) and is perpendicular to the plane x + 2y +…

A:

Q: The line : X - 3t, y = 1 - 2t, z = 2 - t is perpendicular to the plane: X - y - z = 1.[g]

A: Given that equation of line x=-3t ,y=1-2t ,z=2-t and equation of plane x-y-z=1To chaque the line and…

Q: Find the distance from the point (3,-7,-1) to the plane -x + 5y + 2z = 34.

A: Here is the solution:

Q: Find an equation of the plane. The plane that passes through the point (1, 3, 5) and contains the…

A: Given linex=5t , y=1+t , z=3-tDirection vector of this linev⇀=5,1,-1coefficients of t

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: 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: Let L be a line which passes through the point (-5, 0, 1) and is perpendicular to the plane x + 2y +…

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: A) Find the point at which the line x = 2, y = 3+ 2t, z = -2 - 2t meets the plane 6x + 3y – 4z = -12

A: Given line is x = 2, y = 3 + 2t z = -2-2t and the plane 6x + 3y - 4z = -12

Q: Find the plane containing the intersecting lines L1: x = -1+t, y= 2+t, z = 1 – t; L2: x = 1 – 4s,…

A: The given intersecting lines are  L1: x=-1+t,y=2+t,z=1-t; -∞&lt;t&lt;∞L2: x=1-4s,y=1+2s,z=2-2s;…

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 on the plane x+y+z=-46 that is closest to the point (1,1,1).

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 an equation of the plane through the point (2,0, 1) and perpendicular to the line x = 3t, y = 2…

A: To find the equation of a plane passing through (2,0,1) and perpendicular to the line x=3t , y=2-t ,…

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

A:

Q: Find the point at which the line intersects the given plane. x = 3 - t,   y = 3 + t,   z = 2t x - y…

A: Substitute the line equation in the plane equation

Q: Find the point on the plane x+ 2y - z 12 that is nearest the origin.

A:

Q: Find the equation of a plane that passes through the point (0,0,0) and contains the line x = 2 -t y…

A: Here we have to find the equation of a plane that passes through the point (0,0,0) and contains the…

Q: Let L be the line that passes through the point  (1,3,1 ) and orthogonal to the plane 3x-2y + 5z =…

A: In the question we have to find interacting points at which line and plane intersect.

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

A:

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

A:

Q: Find an equation of the plane. The plane that passes through the point (3, 4, 5) and contains the…

A:

Q: Find the point of intersection of the line x = 2 − 3t y = 4 + 2t −∞ &lt; t &lt; ∞, z = 3 − 5t, and…

A: x=2-3ty=4+2tz=3-5tand the plane 2x+3y+4z+8=0

Q: Find the point in which the line through the (3,-1,2) perpendicular to the plane x +2y -5 z = 4…

A:

Q: 8) Determine if the line given by r(t) = intersects the xz-plane. If so, determine at what point.

A: we have to find the point of intersection.

Q: Let L be a line which passes through the point (-7,0, 1) and is perpendicular to the plane x + 2y +…

A:

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

A:

Q: Show that the line through two distinct points (x1, y1) and (x2, y2) in the plane has equation: | x…

A: Solution..

Q: Give the general equation of the plane containing the point (3,-1,4) and x 2-2 perpendicular to the…

A: The given equation of the linex2=y=2-z-3which can be written asx-02=y-01=z-23.The given point is…

Q: Find the general equation of the plane that contains the point (2, 0, 3) and the line x =−1+t, y =…

A:

Q: A) Find the point at which the line x = 2, y = 3+ 2t, z = -2-2t meets the !3! plane 6x + 3y- 4z -12

A: Here we have to find the point at which the line x=2, y=3+2t, z=-2-2t meets the plane 6x+3y-4z=-12…

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

A: The line L is perpendicular to the plane, x+2y+4z = 0 Hence the direction ratios of the line L is…

Q: Let L be a line which passes through the point (-3, 0, 1) and is perpendicular to the plane x + 2y +…

A:

Q: A) Find the point at which the line x = 2, y = 3+2t, z = -2- 2t meets the plane 6x + 3y - 4z = -12

A: The line is given by:x=2, y=3+2t, z=-2-2tand the plane is given by6x+3y-4z=-12.We need to find the…

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

A:

Q: Q2) Find the distance from the point P (1, 2, 3) to the plane x-3y + 2z= 4.

A:

Q: find the point in which the line meets the plane x = 1 + 2t, y = 1 + 5t, z = 3t; x + y + z = 2

A: Given, The equation of line x = 1 + 2t, y = 1 + 5t, z = 3t and the equation of plane is x + y + z =…

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

A: