Find the equation of the plane containing the following two lines: L1 : te R 1 L2 : +s. seR 1

Q: Q3:Find equation of the Plane determined by the inter Sectiny (X-5+2{ ツ=ー!+& そ=C+4) (x=3-t ッ= 6+z4,…

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Q: Find two di¦erent planes whose intersection is the line x = 1 + t, y = 2 - t, z = 3 + 2t . Write…

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Q: Find the points where the liner(t) = 4 − 3t, 8 + 7t, 5 + t, −∞ < t < ∞,intersects each of the…

A: The point where the line intersects co-ordinate planes, one of the co-ordinates must be zero.

Q: Find an equation for the plane that contains the line v = (-1, 1, 2) + t(9, 5, 4) and is…

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Q: Find the equation of the plane through the point (2,4,3)(2,4,3) that is perpendicular to the line…

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Q: Find the equation of the plane that passes through the point (6, 0, −2) and contains a straight r:…

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Q: d. Find the equations of the two parallel planes that are distance 5 away from plane P.

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Q: What angle does the line of intersection of the planes 2x + y - z = 0 and x + y + 2z = 0 make with…

A: Given:The planes 2x + y - z = 0 and x + y + 2z = 0

Q: Which of the following is the equation of a plane parallel to the cz-coordinate plane and passing…

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

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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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Q: Show that the lines determined byr 1(t) = < 7, 3 − 4t, 2 + 6t> andr 2(t) = <6 − t, 3 + 8t,…

A: Given: r1(t)=7,3-4t,2+6t r2(t)=6-t,3+8t,9-5t For r1. x-7=y-3-4=z-26=t For r2. x-6-1=y-38=z-9-5=t…

Q: Ex(29):- Determine whether the line and the plane are intersect; if so, find the point of the…

A: Given, The equation of the line   L : x=t, y = t, z =t  Equation of the Plane : PL : 3x-2y+z-5=0…

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

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Q: Find an equation for the line that is orthogonal to the plane 3x- y+ 2z =10 and goec through the…

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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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Q: Find the Cartesian equation of the plane through the point (5, 1,0) and parallel to the lines = 2+t,…

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Q: Given the planes π1 : x − 2y + 3z + 1 = 0 and π2 : 2x + y + z + 2 = 0. Find the equation of the…

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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 the plane which contains both lines: a. x = 1-4t, y = 1+2t, z = 2-2t b. x = -1+s, y = 2+s, z…

A: Since you posted here 3 questions,  I can answer only first one.  Please reupload remaining two…

Q: Suppose a line is given parametrically by the equation L(t) = (4+ 3t, -4 – 5t, 2 – 2t) %3D Then the…

A: Compare with general equation of line in parametric form

Q: Find an equation for the plane that contains the line x = − 1 + 3t, y = 5 + 3t, z = 2 + t and is…

A: We need to determine the equation of the plane that contains the line: x=-1+3t, y=5+3t, z=2+t and is…

Q: Find the point(s) of intersection (if any) of the plane 2x + 3y = 10 and the line (x − 1)/3 = (y +…

A: The equation of line x-13=y+1-2=z-3=r(arbitarary point) then x = 3r +1 y = -2r -1 z = r+3

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 the point​ (if it​ exists) at which the following plane and line intersect. y=−11​;…

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

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

A: x+ y+ z= 4

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: d. The plane through P,(2,4,5) perpendicular to the line x=5+t y=1+3t .

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Q: Find the equation of the plane which contains the line ( 2 + t , 3 − t , 4 + 2 t )and the point ( 0…

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Q: Find the cartesian equation of the plane determined by the two intersecting lines x-4 y+1 z-2 L1: 3…

A: Here,  v1=3i+2j+kv2=5i+3j+2k v1×v2=ijk321532=i4-3-j6-5+k9-10=i-j-k Thus, the equation of the plane…

Q: (2t+l, st-5, lot ) f 4z: Given two lines ( 34, 2++3, zt+1) located in Sice the plane ? plane, find

A: The required equation for the plane is calculating by the below method.

Q: -1. Through (1,5, 2) perpendicular to 37 – J + 4k .

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

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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: х —7 у-5 z-1 L: 4 -,P: 2x + y – 7z +1 = 0 6. 3

A: Given Data: Line: x-74=y-53=z-16 Plane: 2x+y-7z+1=0 Let t is a constant variable for line,…

Q: Find the points of intersection of the line x = 3+2t, y =5+7t, z = -3+t, that is, I(t) = 3+2t, 5+7t,…

A: To determine the intersection of the line with the coordinate planes.

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 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 for the line passing through and perpendicular to Hhe plane P= (!,2,-3)…

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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,…

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Q: Suppose the plane II is given by the equation A + By +7z = 8, and it is parallel to the lines l1, 2…

A: It is know that if the two vectors are parallel then their dot product is 0. Determine the direction…

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

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