Question Find the equation of the Plane through the point (-1,4,2) that contains the line of intersection of the planes 4х — у +z—2 %3D0 2х + у — 2z —3 %3D 0

Q: Find the equations of the line that passes through point Q(1, 2, 1) and is perpendicular to the…

A: Consider a    plane where represent the direction ratios of the normal vector to the plane.  The…

Q: 2+ 3s -2 – 5s Find the equations of two planes which intersect along the line L(s) =

A: Given the parametric equation of the line be, x=2+3sy=-2-5sz=s Assume the equation of Plane 1 be…

Q: Second question: Let us have the line whose equation is L: X / 5 + 5 = y + 1 = z - 5 (1) Find the…

A: Given: x5 + 5 = y + 1 = z - 5.

Q: Write the equation of a sphere that has a center at C(2, 5,-3) and contains points D(4, 1, 1) on the…

A: Given Data: The centre of the sphere is: C(h, j, l)=C(2, 5, -3) The point at the edge of the sphere…

Q: Which relationship describes the two planes -20 a + 4 y- 8 z = 40 and 15 + 3 y- 15 z = 72? O The…

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Q: Find the point on the plane 2x+ 3y + 6z - 10 = 0 closest to the point (- 2,1,3). The point is ( ID.…

A: see below

Q: The picnic table is located 8 meters from the slide and 6 meters from Holly. The duck and duckling…

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Q: 1- y?. 3. For the system xy (a) Sketch the nullclines and direction arrows. || 一中型出

A: Note: According to Bartleby we have to solve the first question please upload the question…

Q: Let "r" be the line determined by the intersection of the planes x+y-z= 0 and 2x-y+3z-1=0.Find the…

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Q: 5-x 2+y Find the equation of the plane that contains the line = = 5 – z , and the %D 3 point P(…

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Q: 1 2 -3 Let A = 2 4 -6 1 2 -3 (a) Explain why im(A) is a line, and find its equation. (b) Explain why…

A: Given a matrix, A=12-324-612-3 (a) Then, ImA=B=abc|Ax=B, x∈ℝ3. Consider the augmented matrix AB.…

Q: 4. (a) Describe the three-dimensional coordinate system. What are the coordinate planes? (b) What is…

A: * As per our guidelines, we are supposed to solve only the first three problems/subdivisions. Please…

Q: Select the line and the plane whose intersection is a point. A. HI B. FH C. Plane EFH D. Plane AHI

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Q: Section: Equations of lines and planes. Find the plane. The plane that passes through the point…

A: An equation of the plane containing the point (x0,y0,z0) with normal vector N = <A,B,C> is A(x…

Q: How do you find the intersection of two lines in space? A line and a plane? Two planes? Give…

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Q: through the plane? 2 a13 -1 a13 B = a21 -1 a23 and 12. Given A = 3 and B = 4 where A =| a a31 2 %3D…

A: We have to find determinant

Q: After school, Shaquille and Reyna need to pick up their basketball uniforms and return to school for…

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Q: 4. Find the point on the plane 4x+7y+8z-16=0 closest to the point (-3,3,2). The point is (Simplify…

A: we use langrange multiplier method

Q: Model with mathematics. Use the square shown. y A, - 5 a. What are the coordinates of the image of…

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Q: х-2 у-2 2-3 3 1 coordinates of P, the point of intersection. x- 2_ y - 3 _ z – 4 and 1 (a) Show that…

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Q: Determine the distance between point A(-1,-3) and point B(5, 5). Write an equation of the…

A: Answer and explanation is given below...

Q: Question Determine whether the lines L¡ and L2 are equal, parallel but not equal, skew, or…

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Q: 8 Quiz... Summative.. Sign out The Pythago.. a Summary -. Previous 1 v Next The Pythagorean Theorem…

A: Given : On the coordinate plane, line segment VW is given . With coordinates of V(-2, 2) and…

Q: 3. Look at the given picture. Is it possible for two planes to intersect in a point? Explain your…

A: Given: The picture of two planes, To determine: whether two planes can intersect at a point or not…

Q: Find the point on the plane 2x + 5y + 6z - 12= 0 closest to the point (- 3,2,3). ..... The point is…

A: see below the calculation and explanation

Q: 28. y In the figure, 0, A(6, 2), B and C are the vertices of a parallelogram. The diagonals OB and…

A: Here the objective is to find the equation of line AB and BC.

Q: a) 3x+5y-22-4 = 0 4x + 7y+6z+11 = 0 -6x-10y + 4z +8 = 0 b) 5x+3y-z-11 = 0 -2x - 7y +10z-2=0…

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Q: 1) Find a plane through the petints (2,-S,-S), (6,16),(-8,7,4)

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Q: QI: Draw the projections of the points: A (8, 3), B (-5, 4.5), C(0,-3). D (6, -3), E (-5.5, -1), F…

A: Solution is given below:

Q: Question Find the symmetric equation of the line passing through the points (5, 2, -8) and (-10,4,…

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Q: 04.PMA.Geometry.Q3.2021 Question: 1-51 Which equation represents a line on a coordinate plane that…

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Q: Shaquille's house Reyna's house School DRAWING NOT TO SCALE After school, Shaquille and Reyna need…

A: The figure is

Q: 1 2 -3 Let A =| 2 4 -6 1 2 -3 (a) Explain why im(A) is a line, and find its equation. (b) Explain…

A:

Q: 24. The two planes are perpendicular. Find the value of k. I1:X-y+ 2z - 5 = 0 Tg: 3x - 2y + kz + 1 =…

A: We will find the value of k as following.

Q: 4. The planes P1, P2 and P3 are parallel to the coordinate planes. If (xo, yo, Zo) = (3, 2, 4) then…

A: If a plane is parallel to xy-plane and it passes through the point x0,y0,z0 then the equation of…

Q: The roof of a house is represented on the coordinate plane below. B(5,4) A(-7, -2) A builder…

A:

Q: Find the point on the plane 2x + 5y + 8z - 19 = 0 closest to the point (- 2,1,3). The point is ( D:…

A: see below the calculation

Q: Completing a Line Segment Plot the points M = 15, - 42and B = 17, - 22 in the xy-plane. If M is the…

A: We have two points M15, -42 and B17, -22 Point "M" is mid point of line segment AB.

Q: Che z-axiS, (a) the x-axis. 2. Consider the points P(3,0, 1), Q(5, –1,2), R(5, 1, -1), and S(0, 4,…

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Q: The equations of two lines are: L1: r(t) = 2+ t, y(t) = 2+3t, z(t) = 3+t - 3 L2 : 4. (a) Find the…

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Q: 2. Triangle ABC is graphed on a plane. The coordinates are A(-2,5), B(-8,5), and C(-2,-1). If A ABC…

A: Given:     Coordinates of triangle are:         A=-2,5         B=-8,5         C=-2,-1    Reflection…

Q: 2 At a fair there are three hamburger stands, A. B and C. The fairground is in the shape of a…

A: Concept: The midpoint of the two points (x1,y1) and (x2,y2) x1+x22,y1+y22 The slope of the two…

Q: Matching surfaces Match equations a-d with surfaces A-D. a. z = V2r? + 3y² + 1 – 1 c. z = 2r? – 3y?…

A: Given surfaces are,  a) z=2x2+3y2+1-1b) z=-3y2c) z=2x2-3y2+1d) z=2x2+3y2-1 Also we have given with…

Q: a. Find the equation for the line going through points P (1,2,3) and Q (–4, –8,3)

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

Q: Direction: Identify the value of a, b, and c. 1. - 1 2. 9-4)_ (x-5)2 25 16 (x+1)2 O-2)2 3. 49 36 4.…

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Q: Find the point on the plane 4x +7y + 8z - 14 = 0 closest to the point (- 3,2,3). The point is D…

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Q: Completing a Line Segment Plot the points A = ( - 1, 8) and M = (2, 3) in the xy-plane. If M is the…

A: To plot: The points A-1,8 and M2,3 in the xy plane, find the coordinates of B. Given: The point M2,3…

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.