Problem. 1: Find a parametric representation for the plane through the point (-6, 0, –6) that contains the vectors i – 4 j and j – k (Write a, y, and z in terms of u and/or v.) x = -6 + u, y = 2 = ? where ? < u < ? and ?

Q: Question 7 The equation of the sphere with center (5, 6, 5) and satisfied by the point (6, 3, - 1)…

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Q: QUESTION 5 Find a vector equation of the line through point (6.0.2) and parallel to the line with…

A: Given:x=4-3ty=-1+4tz=6+5tPoint 6,0,2

Q: If a line is parallel to the vector 2i + 9j + 8k and passes through the point P = (6, 8, 8), then…

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Q: If a line is parallel to the vector 8i + 5j + 3k and passes through the point P = (6,2,4), then the…

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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 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: a line is parallel to the vector 2i + 7j+ 8k and passes through the point P = (3,6, 6), then the…

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

Q: (d) Find the parametric equation for the line segment from point P(1,3, 2) and Q(1, –1,6).

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Q: QUESTION 10 Let r(t)=(1-t2, 5t, 2t3). Find the z-component of the vector r'(4).

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Q: 1. Which of the following equations is an equation of a hyperboloid of two sheets? A. x^2 − y^2 −…

A: The answers are given below

Q: Question 6 Which of the following is an equation of a plane that passes through the origin (0,0,0) O…

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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: If a line is parallel to the vector 4i + 1j+ 4k and passes through the point P = (3,7,9), then the…

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Q: PROBLEM (7): Find the outward drawn unit normal vector n to the surface (x-1) +y?+(z+2) = 9 at the…

A: To find- Find the outward drawn unit normal vector n^ to the surface x - 12 + y2 + z + 22 = 9 at…

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

A: As per the company guidelines we are supposed to solve first 3 subparts of a question untill…

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: A. Find an equation of the hyperplane H in R° that passes through P(1; 3; 5; -1,4) and is nomal to…

A: Let's see the concept. Concept:- Equation of hyperplane H in R5 that passes through(p, q, r, s, t)…

Q: QUESTION 3 Let r(t)=(1-t?,5t,2t3). r'(3). Find the z-component of the vector

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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: 1) The area of the triangle whose vertices are the points P(1,0,2), Q(3,-1,3), and R(4,1,2). 2)…

A: To find the following equations of line , and area of a triangle.  Since you have posted a question…

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: #15.) Determine the vector, parametric Cartesian equations of each of the following planes: a)…

A: Note:- Since you asked multiple subparts then as per our policy we can solve first three subparts…

Q: (S'34) 9uq Find vector, parametric, and symmetric equations of the line through (2,3,4) and is…

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Q: L(t) The vector parametric equation for the line through the points (1, 2, 4) and (5, 1,-1) is

A: Given points,  (1,2,4) and (5,1,-1)

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

A: Plane problem....

Q: If a line is parallel to the vector 6i + 7j+ 2k and passes through the point P= (5, 1,7), then the…

A: Given that a line is parallel to the vector 6i+7j+2k and passes through the point P=5, 1, 7. We know…

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: 4) a) Find the vector parametric equation of the line in R³ that is perpendicular to the plane 2x -…

A: Given plane is, 2x-3y+7z-4=0

Q: If a line is parallel to the vector 3i + 9j+ 6k and passes through the point P = (5, 5, 4), then the…

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Q: Find parametric equations for the line through the point P(-5,6,7) and perpendicular to the vectors…

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Q: If a line is parallel to the vector 3i + 2j + 1k and passes through the point P = (1,3, 8), then the…

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Q: If a line is parallel to the vector 3i +2j+ 1k and passes through the point P = (1,3,8), then the…

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Q: Question 14 (1 point) ✔ Saved Determine the scalar equation of a line with a normal vector passes…

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Q: Which of the following are equations for the plane through the points P(1, 1, -1), Q(3, 0, 2), and…

A: First find PQ and PR , two lines on the plane

Q: Find an equation for the plane that passes through the point (1, 2, 3) parallel to u = 2i + 3j + k…

A: Given:u = 2i + 3j + k and v = i - j + 2kFirst find cross product

Q: 9. (A) Find the parametric equations for the line through the point P = (-5, -1, -3) that is…

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Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x = 2+3t…

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Q: 6) Find parametric equations for the line through P(0, -2,-2) and Q(1,1,0).

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Q: If a line is parallel to the vector li + lj+ 4k and passes through the point P = (8, 4, 8), then the…

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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: (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: 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: 6) Find the following: a) An equation of the plane passing through the points P(2,1, 10, Q(-1, -1,…

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Q: If a line is parallel to the vector 7i + 5j+ 5k and passes through the point P=(4,3,5), then the…

A: To find the parametric equation of the line:Given line is parallel to the vector 7i+5j+5kSo, a=7,…

Q: Work Problem 2 [ 31 (a)[3 Find a vector equation and parametric equations for the line that passes…

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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