find the point in which the line meets the plane x = 2, y = 3 + 2t, z = -2 - 2t; 6x + 3y - 4z = -12

Q: The point of intersection between the line t with the plane 2x + 3y +5z = 31 is

A: Given line ,x-1-4=y-13=z5=tTherefore any point on the line is of the form (1-4t,1+3t,5t)Put this…

Q: 10. Find the coordinates of the point of intersection of the line L: x = -1+ 3t, y = 2 – 2t, z = 3 +…

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Q: Find any line equation that does not intersect the plane 2x – 5y + 3z 4. -

A:

Q: Find equation of the plane that contains the lines L1:x = 3 + 5t, y = 6+ 2t, z = 6 + 3t and L2: x =…

A: Equation of plane which passes through L1 is ax-3+by-6+cz-6=0 where 5a+2b+3c=0.

Q: Find the equation of the plane through the line of intersection of the planes x+y+z=1and 2x+3y+4z=…

A: The equation of the plane through the intersection of the planes, x+y+z=1 and 2x+3y=4z=5, is…

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

A:

Q: Determine whether the line L : x = 3 – 4t, y= 5+2t, z = 5 + 4t, - is parallel to the plane x - y +…

A:

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 equation for the plane through Po(- 4,8, - 3) perpendicular to the following line. x = - 4…

A:

Q: draw the plane given by the equation  x + y + z = 0

A: x+y+z=0 It is a plane passing through origin.

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: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A:

Q: Determine the equation of the plane that contains the lines Li and L2. L: x = 3- t, L2: x = 8 +2 s,…

A:

Q: Determine the equation of the plane that passes through (2,-4,1) and is perpendicular to the line of…

A: A plane is passing through 2, -4,1 and perpendicular to the line of intersection of the plane  3x -…

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

A:

Q: Find the equation of the plane that contains the line x-y+z=2 , x+y+2z=D4 and the line 1= = 2-7

A:

Q: Find the equation for the plane through Po(6, – 3,7) perpendicular to the following line. x= 6+t, y…

A: Given equation of the lines are, x=6+t, y=-3-5t, z=5t The given equation of the lines can be written…

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 an equation of the plane that contains the line x = −2 + 3t , y = 4 + 2t , z = 3 −t and is…

A:

Q: Find the equation of the plane perpendicular to the line x 2t, y = 6 - t, z = 4+t and containing the…

A:

Q: Draw the plane given by the equation. x + y + z = 4

A: x+ y+ z= 4

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

A:

Q: Find the intersection of the line and plane: 2x + 4y – 3z = 19, r(t) = (-2, 1, –1) +t (1, –1,2)

A:

Q: find the point in which the line meets the plane x = 1 - t, y = 3t, z = 1 + t; 2x - y + 3z = 6

A:

Q: Determine if the line given by r(t)=(-2t, 2+7t, -1-4t) intersects the plane given by 4x+9y-2z =-8…

A:

Q: Find the intersection of the line and plane: 4x + 4y – 3z = 5, r(t) = (1, 1, 1) + t(1, –2, 3) %3D…

A: Given that line and plane are 4x+4y-3z=5  ,rt=1,1,1+t1,-2,3To find :intersection point of line and…

Q: Determine whether the line L: = 3- 2t, y=4+ 2t, z = 5+ 2t. is parallel to the plane a-y+3z 7.

A:

Q: Consider the lines x – 4 l2 : 4 - 1 l1: x= 4 – 3t, y = 2t, z = 1 + 5t , %3D 2 (b) Find an equation…

A: Given that:                        Two lines are: l1: x=4-3t, y=2t, z=1+5t,  l2:x-44=y1=z-12

Q: Find the point at which the line (-2, 2, 1) + t(5, –4, 3) intersects the plane -4x – 4y + z = -5.

A:

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

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

Q: Find the point at which the line (-4, 1,1) + t(2, -5, 4) intersects the plane -5x+ 3y – 3z = -54.

A: the given line is  xyz=-411+t2-54 xyz=-411+2t-5t4t xyz=-4+2t1-5t1+4t

Q: ) At what point does the line: L: x =- t, y = 10 + 3t, z = 4 + 3t intersect with the plane n: x – 2y…

A:

Q: Find the point of intersection between the line r(t) = + t and the plane 4x + 5y + 3z = 5. o a. (…

A:

Q: find the point in which the line meets the plane x = -1 + 3t, y = -2, z = 5t; 2x - 3z = 7

A:

Q: Find the equation of the plane contains the line x=3t,y=1+t, z=2t, and parallel to the line of…

A: Given, the plane contains the lines x = 3t, y = 1 + t, z = 2t and parallel to the line of…

Q: Find the point at which the line (-3, -4,-2)+t(5, -4,-2) intersects the plane -5x +3y+z= -155.

A: Given: line equation: -3,-4,-2 +t (5,-4,-2) Then equation of line from parametric equation is given…

Q: Find the equation of the plane containing the line: x = 2 + 10t, y = 2 – 2t, z = 9 + 4t and parallel…

A:

Q: Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 15 –t and L2 : {…

A:

Q: Write the equation for the plane through the point P(- 4,4,2) and perpendicular to the line x =4+7t,…

A: Explanation of the answer is as follows

Q: Find the distance from the line x = 2 + t, y = -2+ 2t, z = 4 – t and the plane 2x – 3y – 4z = 12…

A:

Q: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2). O…

A:

Q: Find the equation of the line where planes Q and R intersect. Q: x-3y+2z=1 R: x+y+z=-1

A: To calculate the equation of line from the point of intersection of the planes Q and R. Where, the…

Q: what is the equation of the plane perpendicular to the intersection line of the x-2y+2z= 3  and…

A:

Q: Find the equation for the plane through Po(-5, - 8,8) perpendicular to the following line. x= - 5-t,…

A:

Q: Find the symmetric equation of the line that is an intersection of the planes a: x-4y + 2z-2 = 0 and…

A:

Q: Find an equation of the plane that is passing through the point and is perpendicular to the line L.…

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 equation of the plane that contains the point P(-6, 5, 7) and is perpendicular to the line…

A: Use direction ratios of line to find direction ratios of plane. Then use the point to find equation.…

Q: Find the equation for the plane through Po(4,- 5,5) perpendicular to the following line. x= 4 + t, y…

A: ee

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

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.