(a) Find the equation of the plane containing the points (3, –4, 2), (5, 1, –2) and (0, 2, –4). (b) Find the distance between the plane with equation 3x – 2y + z = 10 and the plane parallel to it, which passes through the point (–1, 2, 1)

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: 4 The plane t contains the point P(-1,2, -4) and the line 4:r=(2i-5j-3k)+1(-4ị +2j+k) (a) Show that…

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Q: The equation of the plane passing through the point (0, 0, 4) and perpendicular to 4 is: the line 4…

A: Equation of plane

Q: The equation of the plane that contains the three points (1, 2, 0), (1, 3, 1), and (3, 0, 4) is 6x…

A: Cartesian equation of a plane passing through three non collinear points A(x1,y1,z1), B(x2,y2,z2),…

Q: An equation of the plane passing though the points A(-1;2;0),B(0;1;2) and C(1; -1;0) is: O…

A: It is know that equation of plane passing through points x1,y1,z1,x2,y2,z2 and x3,y3,z3 is…

Q: QUESTION 2 Which of the following describes a different plane than the other three? O a. x +2y+3z 6…

A: The  direction cosines of a) is 1,3,2  For the remaining options direction cosines 1,2,3

Q: 4 The plane t contains the point P(-1,2,–4) and the line 14:r=(2i-5j-3k)+1(-4ị + 2 j+k) (a) Show…

A: Since you have asked multiple subparts, as per our company guidelines we are supposed to answer only…

Q: Question 2 Consider the point P(-2, 1, 4) and the vectors a = and b=. (a) Find the unit vector u…

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Q: Question 1: Determine if the two planes 6x + 18y + 14z = -2 and the plane containing the points (1,…

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Q: Question 2 Consider the point P(-2, 1, 4) and the vectors a = and b=. (a) Find the unit vector u…

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Q: Consider the points P = (2,-1,4), Q=(1,1,1), and R=(3,1,-2) in xyz-space. An equation of the plane…

A: Solution is given bellow

Q: 1. Find the equation of the plane that contains the following points. (2, –1, 4), (3, 2,0), and…

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Q: Question 7. The plane is perpendicular to the vector ỹ = i+j+k and contains the point Р- (3, —4,…

A: solution of the given problem is below...

Q: Question 2. Find the equation of the plane passing through the points (0, 1,0), (2, 1, 4), and…

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Q: QUESTION 5 Let A(-1, 3, 3), B(4, – 1, 0), C(5, 4, –7), and D(2. -1, –1). Find i. the normal vector…

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Q: a)What is the distance between the point A(3,1,-1) and the plane 4x + 4y +7z +2=0 ? b) Find the…

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Q: Question 2 Consider the point P(-2, 1, 4) and the vectors a = and 6=. (a) Find the unit vector u…

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Q: A)Find the equation of the XZ plane. B)Finde the equation of the plane ,each of whose points is…

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Q: 19. Find the Cartesian equation of the plane a) passes through point A(6,- 7, 4) and parallel to the…

A: To find the Cartesian equation of the plane, a)Which passes through the point A6,-7,4 and parallel…

Q: Question 11 (a) Find an equation of the plane passing through the points (0, 1, 0). (-1, 3, 2), and…

A: Given points are x1,y1,z1=0,1,0 , x2,y2,z2=-1,3,2 and x3,y3,z3=-2,0,1

Q: (b) Find an equation of the plane passing through the point A(0, 9,2) and parallel to the plane 13x…

A: Given that, the given point is A(0,9,2) the parallel line is 13x+2y-z=10. To find the equation of…

Q: The equation of the plane containing the points (3,1,3), (4,0,-2), and (11,-5, 12).

A: Here we find the equation of plane using three points.

Q: Find the equation of the plane having the points P(1, 2,5), Q(-2, 0, 1), and R(-3,-4,1). 8x + 2y 5z…

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Q: Question 6 | Let ü = (0, 1,-1), 0 (2,2,0) and w (4, 2, 2). %3D a) Show that a, o and w lie in the…

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Q: Find the equation of the plane containing the points P= (2, 0, 0). Q = (0, 2, 1), and R = (1,0, 3).

A: This question is based on finding equation of plane when we know 3 points of plane.

Q: Question 4 2 Let L be the line with the equation -3 +t 2 and let II 4 3 be the plane with equation…

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Q: C-9: The reflection of the plane 2x-3y+4z-3 = 0 in the plane x- y+z-3=0 is the plane.

A: Topic:- reflection of a plane in another plane.

Q: Question 19 An equation of the line passing through the points P(2,3)P(2,3) and Q(3,8)Q(3,8) in the…

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Q: Question 8 Find the equation of the plane that passes through the points A = (2,4, – 3), B =…

A: Plane problem....

Q: Question 8 An equation of the plane passing through the points A(1,2,3), B(2, 3, 1), C(3, 1,2) is…

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

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. Find an equation for the plane consisting of all points that are equidistant from the points (1,…

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Q: Find an equation of the plane each of whose points is equidistant to the point H(4, 2, 5) and to the…

A: Basic 3D Geometry problem

Q: Find an equation of the plane with the given characteristics. -4 The plane passes through the point…

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Q: At which point does the line described in question 3 intersect the plane described above? (Hint: You…

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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: Example 6: Determine whether the planes 3x+ y- 4z = 3 and -9x-3y+12z= 4 are | orthogonal, parallel,…

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Q: 4 /5 . 135% + - (a) Find parametric equations for the line of intersection of the planes x+2y- = 3…

A: In X plane, put y=z=0 & in Y plane put x=z=0 &in Z plane put x=y=0

Q: 2. Give the parametric system of equations of the line given by the equations: 2x = 4 – 3y = ±1 Give…

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Q: QUESTION 2 What is the best descriptor of the object in three-dimensional space given by the…

A: Solution :-

Q: 2- Find un equation 6f the Plane containing the Points (0,0, 2 ), o (2,q!) (-2,3,3).

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Q: a) An equation of the plane passing through the points P(2,1, 10, Q(-1, -1, 10), and R(1, 3, -4)

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Q: An equation of the plane passing through the points A(-1;2; 0), B(0; 1; 2) and C(1; –1;0) is:

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Q: 2. Find the parametric equations for the line through (3, –2,5) and (2,3,0). 3 Find the equation of…

A: To find the parametric equation for the line through 3, -2, 5 and 2, 3, 0

Q: The general equation of the plane that contains the points (1, 0, 3), (-1,1,-3), and the origin is…

A: Explanation: Given that,  equation of plane ax+by+cz=0and (1,0,3), (-1,1,-3) and (0,0,0) on the…

Q: Question 6 Let ū = (0, 1, –1), ū = (2, 1,0) and w = (4, 1, 1). a) Show that ū, ū and w lie in the…

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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: Find the general equation of the plane containing the points P1(0,0,0) P2(1,2,-1), and P3(-1,1,0)

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Q: QUESTION 2 What is the best descriptor of the object in three-dimensional space given by the…

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Q: 4. Determine the general equation of the plane containing the points P(1, -4, –5), Q(2,0, 13) and R

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