45, 46 and 47 Find the point at which the line intersects the given plane. 4j5.jaj= 2j– 2jjj j =j jt,j z =1+t; x+ 2y – z = 7

Q: 14. 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: 25. Find the intersection of the line [x, y, z] 2х — 4у + 7z —26 %3D 0. [1,4, – 2] + t[1, – 1,3] and…

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Q: Given plane z: 3x+2y+z-3=0, point P(1, -2, 3), and lines 1₁:an 4₂: (3, 6,-5)+(2, 3, 1), find: d) the…

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Q: Find the point​ (if it​ exists) at which the following plane and curve intersect.   z=13​; r​(t)=t,…

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

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Q: 16.) Which of the following lines is parallel to the plane? 2x- y – 4z = 4 (a) x=2+1, y =-2-2t,…

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Q: 3. Find the plane determined by the intersecting lines L: x = -1+t, y = 2+t, z = 1- t; L2: x = 1 -…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Which of the following is the intersection point of the plane 5x- 2y- 3z=0 and X = 6+ 2t the line y…

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Q: The equation of the plane through the point (2, 5, 7) that is parallel to the line 7(t) = 3î + 2 –…

A: Explained below

Q: 9. Write an equation of the plane that passes through (2,0, –3) and (a) is perpendicular to the line…

A: Given: The vectors are: a=-1, -2, 3b=3, 0, -2v=2, -5, -4 The equation of plane is, P=2x+y=z+13

Q: If the plane through the points P(1, 1, -1), Q(3,0, 2), and R(-2,1,0), which of the following are…

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

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Q: Find the point of intersection of the lines given below and then find the plane determined by these…

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Q: 1. Find an equation for the plane through P,(0,2,–1) perpendicular to n = 3i – 2j-k

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Given: planes ¹: 2x - 5y+z=-1 and 2: x + 5y+z=5 intersecting on a line . (a) Determine the symmetric…

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Q: Let P = (-2,0, 5), Q = (3, 1, 1), and R = (0,0, 4) and define a = PÓ and b= PR. Find (d) The…

A: Given three points are: P:-2,0,5, Q:3,1,1, R:0,0,4 The position vectors for the given points are:…

Q: which of the following is the equation of the plane that is passing through the point P(2,2,-2) and…

A: Given P( 2, 2, -2) and planes  x+2y-3z=3 and x+y+z=2

Q: Which of the following is the intersection point of the plane 5x-2y-3z=0 and X = 5-t the line y =…

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Q: . Find the relation between line L and plane P: Question 9. 2x +2y-32-1=0. If they intersect at one…

A: The given plane is 2x+2y-3z-1=0. Find the relation between line L and plane P. 1. The given line is…

Q: Find the point at which the line intersects the given plane. x = 4 – 4t, y = 5t, z = 1 + t; x + 2y –…

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Q: Which of the following is the equation of the plane that is passing through the point P(2, 2, –2)…

A: The equation of the plane passing through the points (x0 , y0 , z0) and perpendicular to a vector…

Q: nd 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 equation of the plane with the given description. Contains the lines r1(t) =〈2, 1, 0〉+〈t,…

A: Find the equation of plane containing two lines: r1t=2,1,0+t1, 2, 3 and r2t=2,1,0+t3, 1, 8.…

Q: 24. The value of the constant 2, for which the plane Ax – 3y + 4z = 5 and the line r = i- 2j – 3k +…

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Q: The equation of the plane through P.(2, 4, :5) perpendicular to the line :X = 5 +t ,Y= 1+ 3t , Z= 4t…

A: (.)  Let the point Px1,y1,z1 and perpendicular line  x-x0a=y-y0b=z-z0c Then the equation of the…

Q: 3. Consider the plane TT: 4x + 3y - 2z + 12 = 0. What is the relationship of the plane to each of…

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Q: Which of the following is the equation of the plane containing the points (2,1,2), (4,1,0) and (5,0,…

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

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Q: If Ax+By+5z=C is an equation for the plane containing the point (0,0,1) and the line X-1=と+2 3…

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Q: Determine the Point OF 3x +y+22 = 45 and the Line witth plaremetre eg dartons 1 = 1+t, y= 3 +2 € ,…

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Q: 6) Consider the plane P : x+y – z = 0 in R³ that contains both the points P(1,0, 1) and P2(0, 1, 1).…

A: • In the first part, we have to use the general Cartesian equation of a line passing through two…

Q: 1 7 Let a, 4 21 and b = 6. 1 2

A: here we can use matrix method to write the equation of plane and then we use the condition that b…

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: Qz: Given two lines (2t+1,5t-s,lot) f ong (34, 2t+3,2+1) 1ocated in Sinde the plane ? plane, find

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Q: 6) = Find the point at which the line intersects the given plane. x =3 - t, y = 2 + t, z = 5t; x - y…

A: Equation of a Line in Parametric Form: where are functions of and is the parameter The equation of…

Q: Q/ Find the angle between the planes (x+y+Z=1)and (x-2y+32=1). And find the Symmetric equations for…

A: We have to find angle between two planes

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,-2) and…

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Q: Find the eguation f Plane that Passes through P(12-1,3) and s Parallel to the Plane 3X++6? ans. 3X+y…

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Q: Which of the following is an equation for the line through the point (2, 3) and perpendiçular to the…

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Q: 12. Let v =|0 and y For what value(s) of h is y in the plane -3 -2 generated by v and v2?

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,-2) and…

A: To find the equation of the plane passing through the point P 2,2-2 and vertical to the line of…

Q: = 30 through the points If the plane ax + by + cz P(4, 1, 2) and Q(2,3, –1) is orthogonal to the…

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Q: Q2: () If a= 2i-3j+k, =2 and =4 ;:find (i) (āxj) (i-j+k).(i) (2-5)-(z+5) (b) Find the distance from…

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Q: 6. There is a line through F and H. 7. The intersection of plane CDEH and plane FGHE is EH8. If W is…

A: 6. There is a line through F and H.7. The intersection of plane CDEHand plane FGHE is EH8. If W is…

Q: 19. Find the angle between the line and the plane of the following equations, X_ y- 2_ 3z+ 3 b. L:…

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Q: Let [] Vị -2 and V2 4 3 k For which value(s) of k will Span{v1, v2} be a plane in R3? A. k= 3 (D.) k…

A: Here, the given vectors are: v1=1-23, v2=-24k Now, the  Span{v1,v2} be a plane in ℝ3 if v1 & v2…

Q: 6.) Consider the points P(-1,2,5), Q(2, –3, 0) and (i) Write an equation of the plane containing t

A: Equation of plane: We know that, the equation of plane that passes through point (x, y, z) is given…

Q: Q2) The seraight s line (1,0, 1) +e(2,1,1) intersect The plane X+2y-3#=0 at the point (O,O. D)

A: