Question 10 Find equations for the planes: a) Passes through P(1,–1,–3) parallel to the plane 3x + y + z = 7.

Q: 10) Find an equation for the plane through Po(0,2,0)perpendicular ton = 31 – k.

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Q: Consider the hyperboliode H defined by the equation:  x^2+y^2−z^2=1 and the point P0=(1,4,4) in H.…

A: We are given the following hyperboloid : x2 + y2 - z2 = 1 And we have to choose the correct…

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: Question 6. Find an equation for the plane which satisfies the given conditions. 1. Passes through…

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Q: Question 3 Find the parametric representation of the straight line that passes through the points…

A: we have to find the parametric representation of the straight line that passes through the points…

Q: Question 3. Find the point of intersection of the lines ix=--1-t, and then find the plane determined…

A: We have to find the intersection point of the lines and equation of plane passing through these…

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 4: A plane parallel to y-axis passing through line of intersection of planes x + y + z = 1…

A: A plane parallel to y-axis passing through line of intersection of planes  x + y + z = 1 and 2x + 3y…

Q: The graph of (x/a) + (y/b) + (z/c) = 1 is a plane for any non-zero numbers a, b, and c. Which planes…

A: The graph of given plane is,

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

A: As you have asked for only the solutions of  question number f. So, I am providing only that…

Q: Question 8 (2 marks) The graph of (=) + (2) + (-) = 1 is a plane for any nonzero numbers a, b, and…

A: Solution

Q: Question 19 Let L be the line passing through the point P-(-1, 2, 2) with direction vector d-[1,-2,…

A: First find the equation is line by given points and direction.  Then assume it T and convert (x,y,z)…

Q: D) Find the parametric and symmetric equations of the line through the points(1, and (-5, 4, 2).

A: Given query is to find the equation of the line.

Q: Question 4 Find the distance between the following points in the plane: a) Distance between (2,-1)…

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

A: We have to find the equation of the plane

Q: 4. Consider the points A(1, 0, 3), B(-1, 5, 2) and C(3, -1, 1). Find the equation of the plane…

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Q: Question 4 2 pts Find the point of the intersection of the plane P: 2х — Зу + 42+14- 0 and the line…

A: Given that  The plane and the line  To find the point of intersection of the plane and the line

Q: The equation of the Plane in the form of Ax+By+Cz+D=0 that passes through points (3,1,-2), (-1,2,4)…

A: Topic :- 3-D  Geometry

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: Problem 4: Find the line equation for the line which passes through (1,3,4) and is perpendicular to…

A: According to the given information, it is required to find the equation of line that passes through…

Q: Problem 3. A plane, P, in R contains the point (-5; –-1; –3) and has normal (2; -4; 2)". Find the…

A: Given that: The point is: (-5, -1, -3)and the normal is: (2, -4, 2)T

Q: Questions 1 - 5. Consider the plane that goes through the point (4, 1, 3) and is orthogonal to…

A: Given that the plane that goes through the point (4,1,3) and is orthogonal to vector (2,3,1) . Here…

Q: . Given the point Q(1,-2,4) and a plane p: 3x + 2y + 6z = 5, find a) The distance from Q to p. b)…

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Q: Find an equation of the plane indicated in the figure. 4 Equation: Y 4 4

A: Equation of plane contains following points, (4,0,0), (0,4,0), (0, 4,4) and (4,0,4)

Q: Question 5, Find points of intersection of the plane 3x + 4u - 7- 24 = 0 with the axes.

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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: 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: 5) Find the distance from D to the plane containing A, B, and C NOTE: Enter the exact answer.…

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Q: QUESTION 4. Find the points on the sphere x' +y +z=1. that are closest to and farthest from 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 1-3 JK in the coordinate plane has endpoints with coordinates (-4, 11) and (8, - 1).…

A:

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: Question 3. Do the lines x=t, and x = 2t - 2, y = 2t - 1, 2 = 3t+1 intersect each other at only one…

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Q: Consider the given diagram, find: (a) The coordinates of point R. (b) The exact distance from S to…

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Q: Question 11 The equation x2 + 4y2 = 4 in three-dimensional space is an equation of %3D which…

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Q: If the chord joining two points (a sec 0,, b tan 6,) and (asec 0,, b tan 0,) y? = 1, then prove that…

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Q: (a) Find the parametric equations for the line segment that joins P(1, 0, 1) to Q(2, 3, 1).

A: Given, P(1,01), Q(2,3,1)

Q: QUESTION 4 Consider the points P =(0,0,0), Q=(4,1,1), and R=(3,1,-2) in xyz-space. An equation of…

A: Given: P=(0, 0, 0)Q=(4, 1, 1)R=(3, 1, -2)

Q: QUESTION 10 The line L(t) = (-1+t,3-t,1-t) intersects the plane x - 2y-z=4 at the point P(2,0, – 2)…

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

A:

Q: Find the angle of intersection of the plane -2x – 3y – 5z = -4 with the plane 5x + 5y + 4z = -5.…

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Q: Question 1 Find the equation of the plane through points P1(-2,1,4), P2(1,0,3) that is perpendicular…

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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: 13. Given the points A(3,5) and B( – 3, – 7), find b. the parametric equations of the line.

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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: Given a plane T with equation x – y – z = -9 and a point Po = (1, –1,2). Find the shortest distance…

A: Given plane T : x-y-z = 9 Point P0 = (1,-1,2) To find →the shortest distance d from P0 to T…

Q: Question 22 Consider the plane T:r-z= 1 and the line 2 3 + -1. Find the equation of the plane that…

A: Solved below

Q: Question 6 of 10 What is the distance between the points (4, 5) and (10, 13) on a coordinate plane?…

A: As we know that; The expression for the distance between two points Ax1,y1 & Bx2,y2 is:…

Q: Question 1. 1.1 Sketch the points (1,5, 3), (0, 2, –3),(-3,0, 2) and (2,-2,–1) on a single set c…

A: To locate a point (a,b,c) we can start at the origin and move units along the x-axis then b units…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.