Problem 7 Find the distance from the point to the plane. (1) (6,0, –6), x – y = 4 (2) (3,0, 10), 2r + 3y+ z = 2

Q: Problem 102 Find the slope of the cardioid r=3+8sin 0 at 0 = 1/6. а. -1 с. -б b. -2 d. -3

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Q: Question 22 Consider the plane n :r-z=1 and the line 2 Find the equation of the plane that cantains…

A: Explained below

Q: 9. Find the equations of the planes that are parallel to 2.x - 2y + z = 5 such that the distance…

A: We will solve the problem.

Q: 5) Find the shortest distance from the point P(3, 2,1) to the plane with 4. equation 2x + 3y – 2z =…

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Q: Find the acute angle between the planes with the given equations. x + y + z = 0 and 2x + y - 2z = 0

A: The angle between two planes a1x+b1y+c1z=d1 and a2x+b2y+c2z=d2 is calculated by using the following…

Q: Question – 6: Travelling Salesman Problem Suppose that 9 points are distributed across a…

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Q: Problem 5: Find the equation for the plane which passes through (1,5,7) that contains the line given…

A: To Determine: Find the equation for the plane which passes through (1,5,7) that contains the line…

Q: Problem 1. Parametrize the following surfaces: (a) 2x + 3y + z = 6. (b) z = 9 – Vx² + y?. - (c) x² +…

A: As per Bartleby's answering policy, we can answer only one question with a maximum of three…

Q: 1. The planes defined by the equations x + 2y – 2z = 3 and 2x + 4y - 4z = 7 are parallel. Find a…

A:

Q: Find the equation of the plane parallel to the intersecting lines (1,2 +t, -3 – 3t) and (1 – t, 2 –…

A: Let, the direction vector of 1,2+t,-3-3t is v1=0,1,-3 and the direction vector of 1-t,2-3t,-3-2t is…

Q: Find the​ distance, d, between the point S(6,9,10) and the plane 10x+7y+1z=60.

A: Answer is 73/5√6.

Q: Find the distance from the point (-1, -1, -2) to the plane - 3x – 2y + 1z = -4. Hint: See "Planes"…

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Q: Find the equation of the plane containing the point P(1, 1, –1) and the line -4+t 1- t 1+t

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Q: Find the equation of the plane through the point P = (2, 5, 4) and parallel to the plane 5x – 5y +…

A: Equation of plane parallel to 5x -5y +3z = 6  is given by; 5x -5y +3z + λ  = 6 Also it passes…

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: Problem 2. Identify the following surface by bringing it into a "standard form". Show all the work!…

A: Consider the provided equation,

Q: 15. Find an equation of the plane through the point (-2, 4, 6) and perpendicular to the line r = t,…

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Q: Find the equation for the line passing through P = (2, -2, 1) and perpendicular to the plane -x + y…

A:

Q: Find an equation for the plane through P0(-3, 0, 7) perpendicular to n = 5i + 2j - k.

A: given that the plane passes through (-3,0,7) perpendicular to n=5i+2j-k. we need to find the…

Q: 3. Find the distance from P(1, 1, 1) to the plane II with equation r – 3y + 4z = 10.

A: Distance between point and plane is (4√26)/13.

Q: Problem 11 Consider a plane P described by z = ax+by +c, where a, b and c are constants. Suppose an…

A: The solution is given below

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: 1. Find the equation of the plane that contains the line point (1,3, 2). 무 =D북3부 md the

A: Let's find.

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: 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: Problem 7. Let Q(3, 1, -6) and let I be the line passing through the point Q and perpen- dicular to…

A: We have to find the equation of line L.

Q: QUESTION 4. Find the points on the sphere x' +y +z=1. that are closest to and farthest from the…

A:

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

A: Plane problem....

Q: Question 2. (a) Prove that the lines with parametric equations: x = 1+t, y =1+ 6t, z = 2t and x = 1+…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: :) Find the shortest distance from the point P(3, 1, 1) to the plane with equation 2x – 3y + 2z = 22…

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: 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: Problem 1. Find an equation of the plane that contains the line x = 3+t y = -2+ 5t teR and the point…

A:

Q: An equation of a plane P passes through the point (0,0,3) and perpendicular to the line L:x =1– 2t,…

A: Given,          An equation of a plane P passes through the point 0,0,3 and perpendicular…

Q: ) Find the equation of the plane passes through the point P(2, 2, 3) and perpendicular to the two…

A: To find the equation of the plane that passes through the point P (2, 2, 3) and perpendicular to the…

Q: 13. Consider the point P(3,2,1) and the plane given by the equation 3x +2y+z=0 on the plane closest…

A:

Q: Problem 1. Parametrize the following surfaces: (a) 2r +3y +2 = 6. (b) 2 = 9 - V + y?. (c) r + = 4.…

A:

Q: QUESTION 1 For the parametric line L: x = 4+t, y = 3+t, z= 3-2t and the plane P: -y= x+ z + 2, then…

A: topic : line and plane line and plane are parallel to each other

Q: Find the acute angle between the planes with the given equations. 3x - y + 2z = 5 and x + 4y- z = 2

A:

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

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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: Find an equation of the plane that is passing through the point and is perpendicular to the line L.…

A:

Q: Problem 6. Let P(1, -2, 4) and v = (3, 1, –5), and let l be the line passing through P and in the…

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Q: 4) Find equations for the planes: a. The plane through P(0,2,-1) normal to n = 3i-2j-k

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Q: Question 4. Find an equation of the line of intersection of the planes -x+2y+z= 1 and x+y+z=0.

A: This is a problem related to geometry. Based on the general formula and concept we will answer the…

Q: Problem 1. ad the points on the sphere r² + y² + z? = 9 that are closest to and farthest away

A: Given,           x2+y2+z2=9                        (1)

Q: Find the equation of the plane that contains the point P(3,5, –1) and the line = 4 – t, y = –1+ 2t,…

A:

Q: Problem 1. Find the equations of the items described below A. Any specific line that is…

A: To find the line equation that is perpendicular to the below line. rt=2,−1,8t+3,3,3