6. If the plane ax + by + cz = 30 through the points P(4, 1, 2) and Q(2,3, -1) is orthogonal to the plane 2x +3y- 4z = 5, what is the value of a +b+e? (a) -37 (b) -23 (c) 23 (d) 37 (e) 45

Q: Find an equation for the plane which contains the point P(2,1,- 3) and intersection line of the…

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Q: 5. Find the equation of the plane containing the points P(3, 2, 1), Q(2, 1, -1), and R(-1, 3, 2)

A: Let position vectors of point P(3,2,1) , Q(2,1,-1), and R(-1,3,2) are a→,b→ and c→

Q: The plane equation that has 3.9 units distance to the plane 5x -2y + 3z= 4 is O a. 5.0x-4y+3z=56.1 O…

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Q: Find an equation of a plane containing the line r = (4, –5, –4) + t (–7, 8, –4) which is parallel to…

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Q: Consider the line L: (x-18)/3 = (y-3)/10 = (z-10)/ k, with k ∈ R - {0} and the plane π : 18x + 15y +…

A: The normal of plane will be perpendicular to the given line.

Q: (1) Find an equation for the plane that passes through the point (–1,2,2) and contains the line of…

A: Given: Equation of planes x+y-z=5⇒x+y-z-5=0 and 3x-y+5z=3⇒3x-y+5z-3=0 and point -1,2,2, To find: The…

Q: A linear combination of of u = 3 and v= 4 will give a plane in R³. Given that the point (2, 1, −1)…

A: Consider the given linear combination, u=132 and v=-144 will give a plane in ℝ3. The equation of a…

Q: What is the point of intersection of the following line and plane: line: 7 = [3, 1, 2] + t [1, - 4,…

A: Given  r⇀=3,1,2+t1,-4,-8& plane π=4x+2y-z-8=0 To find point of intersection:

Q: Find an equation of the plane passing through (0,-2,3) that is orthogonal to the planes 2x+ 2y-5z 0…

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Q: Find an equation of the plane passing through the three points give P = (4, –1, 2), Q = (1, 1, 1), R…

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Q: If the plane contains the points P(1, 0, 0), Q(3, 2, 0), R(0, 2, 1), W(a, 1, ), then a = -6 O-2

A: Solution: The equation of plane passing through points P1,0,0, Q3,2,0, R0,2,1 is x-y+3z-1=0

Q: 37 Find the equaton of a plane that contains the point (4, -3, –1) and is perpendicular to the…

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Q: Find an equation of a plane passing through the points (1, –1, 7), (3, 2, –20) and perpendicular to…

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Q: Find an equation of the plane through (-7, 2, –6) that is perpendicular to the planes 4x – y + z = 4…

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Q: 4. How many solutions are there between the plane P₁: (x, y, z) = (4, −3,−1) + s(1, -3,1) + t(2,4,…

A: Plane and line

Q: 39. The plane that passes through the point (1, 5, 1) and is perpendicular to the planes 2x +y - 2z…

A:

Q: Find an equation of the plane passing through (0,-1,3) that is orthogonal to the planes 3x+4y-2z=0…

A: Let's find equation of the plane.

Q: 4-) Find the a Cute augle between the liue joning the two Points AC42,3),B(5,1,7) , and the Plane…

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Q: 1. Determine the point of intersection between the line, L: x = 3+t, y=4-5t, z=1-7t, te R, and the…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 9. Find the equation of the plane through P(1,1,4) that is parallel to the plane x+ 5y – z + 8 = 0

A: The scalar equation of parallel planes differ only by a constant Therefore, equation of the required…

Q: The plane equation that has 2.5 units distance to the plane 5x- 2y + 3z = 4 is %3D O a.…

A: Option (d) is correct.

Q: 1. Find the equation of the plane that passes through the points P(2,0,1), Q(1,0,-1) and R(3,0,1).

A: We have, Vectors in the plane are, Therefore, equation of plane passes through 3 points will be,…

Q: 4. Find an equation of the plane that passes through the points P(1,3,2), Q(3,–1,6), and R(5,2,0).…

A: Given points P1,3,2, Q3,-1,6, R5,2,0

Q: 4-) Find the a Cute augle between the liue joning the two Points ACY2,3),B(5,1,7) , and the Plane…

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Q: 4. Find an equation for the plane in R spanned by the points (1, 5, 1) and (1,4, 2).

A: Given v1 = (1 , 5 , 1)v2 = (1 , 4 , 2) Let xyz be a point in spanv1 , v2 , so there exist m , n…

Q: 5) Determine whether the plane 3x – 4y + 5z = 0 and the plane - 6x + 8y – 10z - 4 = 0 are in…

A: We find out the results by using vectors in 3D

Q: Determine a direction vector of the line of intersection of the two planes 3x + 2y + 5z = 4 and 4x -…

A: The planes are given as- 3x+2y+5z=4........14x-3y+z=-1.........2 Solving both equations for x-…

Q: What is the equation of the plane containing point (3,0,4) and orthogonal to the line…

A:

Q: 19. (1) Give the equation of the line going through (3,2, 7) and orthogonal to r+ 2y - 3z = 16 (2) *…

A: 19) 1 Equation of ine through x0,y0,z0 having direction ratios a,b,c is x-x0a=y-y0b=z-z0c

Q: Find an equation for the plane passing through the points Q(2, 1, –1), R(-1, 3, –1), S(3, 1, 0). 1.…

A: We know that equation of a plane is given by ax+by+cz+d=0 As it passes through (2,1,-1), we get…

Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x y+z=2…

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Q: 1. Find the equations of the planes that are exactly 4 units from the plane 2x-2y+z=6

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Q: Find an equation of the plane that passes through the point (1,2,3) and which is orthogonal to the…

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Q: The planes 3x + 6z = 1 and 2x + 2y - z = 3 intersect in a line. Show that the planes are orthogonal.

A: Given: 3x+6z=12x+2y−z=3

Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x - y + z…

A: To Find : Equation of plane passing through (-3,8,-8) that is perpendicular to the plane7x-y+z=2 and…

Q: 4. What is the equation of the plane through (1 ,2,3) parallel to the plane x- 2y + 3z = 9? (a) x 2y…

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Q: 4. What is the equation of the plane through (-1,-1,0) parallel to the plane x + 2y + 3z = 9? (а) х…

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Q: What is the equation of the plane containing point (3,0,4) and orthogonal to the line WWWw…

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Q: 1. Find the plane which contains the point M (4, 5,0) and the line 2+3 = ¹ = 2²

A: To find the plane which contains the point M4, 5, 0 and the line x+35=y-4-3=z-22.

Q: 3. Find an equation of the plane passing through the points P = (5,1,1), Q = (1,1,2), R = (2,1,1)

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Q: 4. What is the equation of the plane through (-1,-1,0) parallel to the plane x + 2y + 3z = 9? (a) x…

A: To find the equation of the plane through (-1,-1,0) parallel to the plane x+2y+3z=9

Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x-y + z =…

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Q: The equation of the plane that passes by P(-1, 2, 1) and that is perpendicular to the line x - 3 1-…

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Q: Find a plane containing the point (2,-1,3) and the line of intersection of the planes 5x + 7y – 6z =…

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Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x– y + z =…

A: This question is based on finding direction cosine using dot product as two perpendicular plane is…

Q: 4.) a. Find the point of intersection of the line through (1,-5,1) and (5,-12,6), and the plane…

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Q: 3) Find an equation of the plane which contains the points P(-1,2,1), Q(1, –2, 1) and R(1,1, –1).

A: Equation of a plane passing through 3 points P(x1,y1), Q(x2,y2) and R(x3,y3) is given by,…

Q: 5) Determine whether the plane 3x – 4y + 5z = 0 and the plane – 6x + 8y – 10z 4 = 0 are in…

A:

Q: 3. If (4x + 5y+ 7z = 14) is equation of a plane and (x = 2 + 2t, y = 1– 3t, %3D z = 2 + t) is…

A: