6. Find a plane with the P (3, – 4, 5) and contains the line L:= =*

Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Given, through the point (4, 2, -5) and perpendicular to the plane…

Q: of the tss plane passes threngh the point Cl,) and contains the line {x=t, Find the 9 =-2, 2= 2

A: According to the given information, it is required to find the equation of plane.

Q: Determine the value(s) of k such that the lines 2y= -kx +6 and 3y-x= 2kx+3  are perpindicular.

A:

Q: A________ is the set of points P in the plane such that the ratio of the distance from a fixed point…

A: The conic section is known as the set of points, in which the curve of any of the conic, that are,…

Q: 4. Prove that the midpoint of the line segment connect- ing the points (x 1, X 2, - . . , Xp) and…

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Q: 10. Suppose that II1 and II2 are parallel planes in R’, given by: Il : ajx + bịy + C1z = di, and II2…

A: Given two plane which are parallel  Π1:a1x+b1y+c1z-d1,  Π2:a2x+b2y+c2z-d2 and another plane is…

Q: 3. If a plane contains two distinct points Pi and P2 then show that it contains every point on the…

A: Solve the given

Q: 4- Find The cquation ofthe plane That pass hrangh the origin audat the poiat p(11)ond at is parallel…

A: To find the equation of plane passing through the origin, the point (1,1,1) and parallel to the line…

Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,,n2, n2),B(m,,m2,m3),C(r,,r2, 13).

A: Please see the explanation below

Q: Find the distance from (4, –2, 6) to each of the following. a. The xy-plane

A:

Q: If a plane contains two distinct points P1 and P2 then show that it contains every point on the line…

A: From Geometry: Line can be parallel to plane, intersect the plane or lie in the plane. Only third…

Q: Determine the value(s) of k such that the lines 2y= -kx +6 and 3y-x= 2kx+3 are parrallel.

A:

Q: Let C be the oriented line segment starting at (0,0) and ending at (1,2). Calculate Sa F .n ds,…

A: To calculate the below line integral. ∫CF⋅nds Here Fx,y=y,−x C be the oriented line segment…

Q: In the following problems, L is a line, E is a plane containing L, and H1 and H2 are the half-planes…

A: Since, you have post multiple part here. I am answering first one. Please post again for remaining…

Q: 1. Determine whether the lines L₁ given by z=t, y=1 with -∞ <t<∞o) and L₂ given by z=2+s, y = 3-2…

A: Introduction: If two lines are parallel then the ratio equality is true between them. And if two…

Q: 4. Find a plane through Po(2, 1, –1) and perpendicular to the line of in- tersection of the planes…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 4- Find The equation ofthe plane That the origin andat the poiat p(u1)ond at is parallel to theline…

A: Equation of plane

Q: Consider the line L(t) = (-5 – 3t, –1 – 4t,4+5t). Then: L is ? to the plane 7y – 21x – 7z = 63 L is…

A: Given the line  L(t) = -5-3t, -1-4t, 4+5t ⇒ L(t) = -5, -1, 4 + -3t, -4t, 5t ⇒ L(t) = -5, -1, 4 + t…

Q: Sketch the following planes in the window [0, 5] × [0, 5] × [0, 5]. The plane parallel to the…

A: First obtain the plane that parallel to the xz-plane containing the point (1, 2, 3).…

Q: Find the plane through P = (4, −1, 9) containing the line r(t) =〈1, 4, −3〉+ t〈2, 1, 1〉.

A: The plane contains the line r(t)=1, 4, -3+ t2, 1, 1, so a vector in the plane is 2, 1, 1. The line…

Q: Determine the way in which the line [x, y, z] = [2,−3, 0] + k[−1,3,−1] intersects the plane[x, y, z]…

A:

Q: Find the eguatien of the tangett line and nemat plane to the cune; Y. cest Ces(zt)i + st sinCet) j +…

A: Given r=cost cos2ti+cost sin2tj+sintk

Q: 1. How can two pencils (representing lines) be held so that a plane can be passed containing both;…

A: Please submit parts 2 and 3 separately for them to be answered. For the first part, Two lines, in…

Q: 10) Find the point of intersection of the lines L4:x = 1+ 2t, y = 2 + 3t, z = 3 + 4t and L2: x = 2 +…

A:

Q: A. Use the figure on the right to name each of the following: 1. three collinear points 2. three…

A: A) 1) Collinear points are the points which are on the same line. Hence 3 collinear points are A , P…

Q: 34) Show there is no plane perpendicular to n= î +î that passes through points P(1, 2, 3) and Q(2,3,…

A: Since you have submitted multiple question, we will solve the first question for you. To get the…

Q: In the Argand's plane what is the locus of [3(22²-5z + 3) 11_2π ong

A:

Q: Find an cqu of fangat plane the to the gapu xー4y+ プい16

A: Let f(x, y, z) = x2 - 4y2 + z2 - 16 . Let (a, b, c) be a point lies on the given surface.  That is…

Q: Let L be the line that passes through the point  (1,3,1 ) and orthogonal to the plane 3x-2y + 5z =…

A: In the question we have to find interacting points at which line and plane intersect.

Q: If l,, l2, and l3 are nonconcurrent lines, prove that there exist three points. Exactly one each…

A: Three or more points are said Lto be collinear if they all lie on the same straight line If l1 , l2…

Q: 7. Reflect parallelogram RSTU with vertices R(-2, 3), S(2, 4), T(2,-3), U(-2,–4) in the line y = -x.…

A: Reflection in Y axis  : (x , y ) → (-x , - y )

Q: 12) Find the intersection of the plane: x – z = 6, and the line r(t) = (1,0, -,1) + t(4,9,2)

A:

Q: 4. Find an equation for the plane in R³ spanned by the points (1,5, 1) and (1, 4, 2).

A: The two vectors are given as v1 = 151v2 = 142 Let xyz∈span{v1 , v2} Then xyz = mv1+nv2= m151+n142=…

Q: Find the Polnt otintersectton of the lines: l,: x = 2+t, y =3+2t,z z 4 +3t X = S+ 2, y= 2S+4, 2=…

A: Here we will find the point of intersection of given lines,

Q: et y = [ 2   3   -1] and u = [ 2   -6   -6] compute the distance d from y to the line through u and…

A: first we shall find equation of line then find distance from line of that point

Q: (10) Find the distance of (3,-1,2) from each of the following: a) line: x = 1+ 2t, y = -t, z = 1-t…

A:

Q: Find the equations of the tanget plane and normal line to the graph of In(2?)x-을=3y3-VE at the point…

A: Equation of tangent plane f(x, y, z) = k at x0, y0, z0 is, fxx0, y0, z0x-x0+fyx0, y0, z0y-y0+fzx0,…

Q: Find and describe the intersection of the following line and plane: T:2x+3y-4z =-7 and r = (4,2,5)…

A:

Q: Find the equations of the tanget plane and normal line to the graph of In(z?) x - = 3y3 – Vx at the…

A: tangent plane and normal line

Q: 3. If a plane contains two distinct points P1 and P2 then show that it contains every point on the…

A: The given problem can be proved both by mathematically and by the definition. For your convenience I…

Q: Let y = [3] and u = [2] to the line through u and the origin. Compute the distance from y

A:

Q: 5. Find a plane through the points P(1,2, 3), P2(3, 2, 1) and perpendicu- lar to the plane 4x – y+…

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Q: There are 8 points in a plane, and no three points are collinear. These 8 points, taken 2 at a time,…

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Q: A normal equation of the plane that contains the line 1₁: (x, y, z) = (1, -1, 2) + t (9, 1, 3), t E…

A:

Q: Di+Oj

A:

Q: Find the distance between the skew lines r(t)=⟨3,−2,−4⟩t+⟨−4,−2,5⟩ and p(s)=⟨5,2,1⟩s+⟨−6,4,7⟩

A: Given r(t)=⟨3,−2,−4⟩t+⟨−4,−2,5⟩ and p(s)=⟨5,2,1⟩s+⟨−6,4,7⟩

Q: Find the value of o(4x + y)dy - rydy where C is the path around the triangle in the counterclockwise…

A: According to our guidelines we can only answer one question at time, rest you can repost. The given…

Q: Find the general equation of the plane passing through P(−1, 3, −2) and having n = (−2, 1, −1) as a…

A:

Q: 3. If a plane contains two distinct points P1 and P2 then show that it contains every point on the…

A: