Find the equation of the plane that passes through the point (6, 0, −2) and contains a straight r: straight r:   x = 4 - 2t                       y = 3 + 5t                       z = 7 + 4t

Q: Find the point, P, at which the line intersects the plane. x= - 3+ 10t, y = 9- 9t, z= 9- 7t; - 10x +…

A: The objective is to find the point of P, at which the line intersects the plane.

Q: (d) Find the Cartesian equation of the plane that contains both the line L2 and the point A

A: Introduction: The scalar product of two vectors OA and OB is given by, OA·OB=OAOBcosθ The vector…

Q: Find the coordinates of the point where the line F = (1+ 2t)i + tj – 2tk intersects the plane 2x – y…

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Q: Find the equation for the plane through Po(7.- 3. - 1) perpendicular to the following line. x=7+t,…

A: Ans     equation  of  line          x=7+t,   y=-3-3t,  z=-2t  or   x-71=y+3-3=z+0-2

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

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Q: Find the point on the plane 5x+3y+: =11 that is nearest the origin. What are the values of x, y, and…

A: Given: The equation of plane 5x+3y+z=11, To determine: The point on the plane that is nearest the…

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

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Q: Find the equation of the plane that contains the line x=-1+3t, y=5+2t, z=2-t and is perpendicular to…

A: topic - equation of plane

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(4,9,8) perpendicular to the following li x= 4+t, y = 9+…

A: Given x=4+t  , -∞<t<∞y=9+2tz=-5tx=t=x-41 , y=t=y-a2  , z=t=-z5

Q: Find two different planes whose intersection is the line x = 1 + t, y = 2 – t, z = 3 + 2t. Write…

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Q: Find the point at which the line x=1+t, y=3-2t, z=1-t intersects the plane 2x+3y+3z=0

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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,…

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Q: O Find an equation for the plane throught (l,-l,3) parallel to the plane 3x+y+Z=7

A: 1) To find the equation of the plane passing from (1,-1,3) and parallel to the plane  3x+y+z=7

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

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Q: Find the point at which the line intersects the given plane. x = 2 − 2t,    y = 3t,    z = 1 + t;…

A: Given that  x = 2 − 2t,    y = 3t,    z = 1 + t;    x + 2y − z = 4 first we will substitute values…

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

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

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Q: Find the point of intersection of the line l: x = 2+ 3t, y = 1 – 6t, z = 4 – 2t with the plane - 2x…

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Q: Find an equation of the plane that crosses the x-axis at 3, the y-axis at 2, and the z-axis at 5.

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Q: Find the point of intersection of the line x-9 = - 5t, y +1= -t, and the plane 2x – 3y + 4z + 7 =0-…

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Q: Find the equation for the plane through Po(4,9,-7) perpendicular to the following line. x-4+t,…

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

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

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Q: Find the general form of the equation of the plane containing the point Q(0, –2, 10) and the lin l1…

A: Let's find.

Q: Find the equation of the plane that contains the following two lines: I = -1+t, L1 : y = -t, I = -1,…

A: To find the equation of plane containing both the lines

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 distance between the given parallel planes x- 2y + z = 4, 5x – 10y+5z = - 10 2 a. V14 1 b.…

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

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

A: Given:   Plane→   2x+3y = 10  Line→       x-1 3= y+1-2 = z-9

Q: Find an equation for the plane that passes through the point (-1, 6, 0) perpendicular to the line x…

A: Direction ratios of line x =-1 + t, y = 6 - 2t, z = 3t are  <1,-2,3> .Sine line is…

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

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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: Find the intersection of the line and plane: x + 3y – 4z = 18, r(t) = (-3, 2, –2) + t(-3, 2, – 1)…

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

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

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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 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: :: Find the y-coordinate of the point on the plane x+ 6y + 7z = 3 that is closest to the point (-14,…

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Q: . Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 2+8 L1 : 4 -t…

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Q: Find the point of intersection of the lines L1 and L2 and determine the equation of the plane that…

A: Point of intersection of two lines in 3D

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 containing the following two lines: L1 : te R 1 L2 : +s. seR 1

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Q: Give the general form of the equation of the plane that is perpendicular to the plane x+2y x-4 1-2y…

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Q: Which of the following planes is the equation for the plane with an x-intercept at P(2,0,0), a…

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

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