34) Show there is no plane perpendicular to n= î +î that passes through points P(1, 2, 3) and Q(2,3, 4)

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: 7. Let ui (1,4, 2), из (0, 3, 1), из — (1,1, 1), ид — (1, 3, —3) represent four 6. points in the…

A: Since part (i) is very lengthy, we solve first part only. For other part please resubmit.

Q: Show that except in degen-erate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w)…

A: Show that except in degenerate cases, (u x v) x w lies in the plane of u and v, whereas u x (v x w)…

Q: 1- Determine the Eq. of plane (M) pass through points A(0,2,0), B(1,1,1), C(-1,0,2)

A: Hi there! Thank you for the question, but as per our guidelines, we can solve only one question at a…

Q: b) Show that the points A = (1, 2, 2), B = (3,4, 5) and C = (-1,0, –1) lie on a plane through the…

A:

Q: 1. The plane containing the point (1,-5,8) and orthogonal to the line given b x=-3+15t, y=14-t,…

A:

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: Compute the orthogonal projection of i -5 onto the line L through -4 and the origin. proj, (5) =

A: Here we use for product to find he projection.

Q: Let U(9, 9, 2), V(9, t, 4), and W(2, 5, 8). U, V and W have the same starting point. find t for…

A:

Q: Determine the Eq.  of plane (M) pass through points A(0,2,0), B(1,1,1), C(-1,0,2)

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Q: 1 Compute the orthogonal projection of v = onto the line L through -6 and the origin. 2 projz (7) 2.

A:

Q: If the plane contains the points P(1, 0, 0), Q(3, 2, 0), R(0, 2, 1), W(a, 1, ), then a = -6 O-2

A: Solution: The equation of plane passing through points P1,0,0, Q3,2,0, R0,2,1 is x-y+3z-1=0

Q: 20) Find the equation for the plane in 3-space passing through the points (2,3,2), (0, -4, 3) and…

A:

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: 49. The line through the point t (0, 1, 1) that is orthogonal to both (0, -1, 3) and (2, –1, 2).

A:

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]…

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Q: Indicate on an xy-plane those points (x, y) for which the statement holds. |x − 3| ≤ 5 and |y + 2|…

A:

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: 8. Which line does not lie on the plane r = (1,5,0) + s(2,-3,1)+t(1,−1,4), s,t € R? a. V = (1,5,0) +…

A: To Find: Which of the given lines does not lie on the plane r = (1,5,0)+s(2,-3,1)+t(1,-1,4) where…

Q: show that the pants AC1,1,4), B(2,2,2), c(o,l,5) and D(1,0,5) coplanear (in the are Same plane).

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Compute the orthogonal projection of = 3 onto the line L through -2 and the origin 2 proj, (v) =

A:

Q: 2. Use a directed line segment to represent the vector. (а) и %3D (2, —4) (b) v = (2,4, –4)

A: Given that the vector a u=2,-4  b v=2,4,-4Solution a u=2,-4u=22+-42u=20  =25b v=2,4,-4v=22+42+-42v=6

Q: If the plane F contains the points P(1, 0, 0), Q(3, 2, 0), R(0, 2, 1), L O 1 6 -6 O -2

A:

Q: Show that F(z, y) = (ry, z°y?) is not path independent by considering the line segment from (0,0) to…

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Q: 11. Given the coordinates X(0,0), Y(6,3) 0/4 and Z(2,1), find the ratio where point Z partitions the…

A: Use Section formula to solve this question. According to section formula: let coordinates of X is…

Q: (31) Find a plane through A(2, 1, –1) and perpendicular to the line of intersection of the planes 2x…

A: Given, 2x+y-z=3 ,x+2y+z=2 The equation of the plane passing through x1,y1,z1 is given by…

Q: 4. How many solutions are there between the plane P₁: (x, y, z) = (4, −3,−1) + s(1, -3,1) + t(2,4,…

A: Plane and line

Q: 39. The plane that passes through the point (1, 5, 1) and is perpendicular to the planes 2x +y - 2z…

A:

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

A: This is the rough image Point P(1,2,3) and Q(2,3,4) are the points on the plane…

Q: Determine the way in which the line [x, y, z] = [5, −9, 3] + k[1, −12, 2] intersects the plane [x,…

A: Determine the way in which the line [x, y, z] = [5, −9, 3] + k[1, −12, 2] intersects the plane [x,…

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: 39. The plane that passes through the point (1, 5, 1) and is perpendicular to the planes 2x + y – 2z…

A: Given:

Q: A plane through the three points P = (4, -3, 5), Q = (-2, -3, 5), and R= (-2, 3, -3) is described by…

A:

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

A: Given v1 = (1 , 5 , 1)v2 = (1 , 4 , 2) Let xyz be a point in spanv1 , v2 , so there exist m , n…

Q: ortho ne plane through the points -1,0,0), (0, –1, –2), 2, 3, 4) is

A: Please refer to the image below

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: 2. Find the eanation of the plane Containing the point (2,3,3)'and the line Of intersÉCtion 'of the…

A: We have to find the equation of plane containing the point (2, 3, 3) and the line of intersection of…

Q: 3) Find the plane through the points: A(2, 4, 5), B(1, 5, 7) and C(-1, 6, 8)?

A: Let the given points are:

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: Select all lines that are parallel to the plane x+y+z%= 3. OF(t) = (1,1, 1) + t(1, 1, –2) OF(t) =…

A:

Q: 1 Find the plane through the points A(1,2,-), B(4,2,-2) and C(2,3,4)?

A: We are given the points : A(1,2,14) , B(4,2-2) and C( 2,3,4) Equation of a plane passing through…

Q: Compute the orthogonal projection of i = 1 onto the line L through 4 and the origin. projz (5) =

A: Vector projection

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

A:

Q: 8. Which line does not lie on the planer = = (1,5,0) + s(2,-3,1)+1(1,-1,4), s,t € R?…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

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

A:

Q: Find points in the Euclidean plane corresponding to the points e₁-[3,-5,-1], e2=[1,-2,2], e3 [2,1,0]…

A: By Pn , we denote the projective space of dimension n, defined as follows: Pn=Rn+1 \ {0}~, where '~'…

Q: (5) Let 8. u = 6. --(:)- and y = 1 What is the orthogonal projection of y to the line through u and…

A:

Q: Suppose that II1 and II2 are parallel planes in R³, given by: II : ajx + biy +cjz = d1, and II2 :…

A: If ∏1: a1x+b1y+c1z=d1 and ∏2: a2x+b2y+c2z=d2 are parallel planes, then, the cross product ∏1×∏2=0.…