Let a be the plane that contains the points A(-3, –2,5), B(0, 1, 7) and С (4, — 1,2). i. Find the angle of BCA. ii. Find the equation of the plane T. iii. Find the shortest distance between a point Q(5, 8, 10) and the plane T.

Q: Find the points where the liner(t) = 4 − 3t, 8 + 7t, 5 + t, −∞ < t < ∞,intersects each of the…

A: The point where the line intersects co-ordinate planes, one of the co-ordinates must be zero.

Q: Given plane z: 3x+2y+z-3=0, point P(1, -2, 3), and lines 1₁:an 4₂: (3, 6,-5)+(2, 3, 1), find: d) the…

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Q: O Find an equation for the plane Hhrought (1,-1, 3) parallel to the plane 3xay+Z=7

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Show that the lines determined byr 1(t) = < 7, 3 − 4t, 2 + 6t> andr 2(t) = <6 − t, 3 + 8t,…

A: Given: r1(t)=7,3-4t,2+6t r2(t)=6-t,3+8t,9-5t For r1. x-7=y-3-4=z-26=t For r2. x-6-1=y-38=z-9-5=t…

Q: For the points A(2, 1, 1), B(1, 1, 2), C(0, 1, 0) and D(5, 4, 6), let M be the plane containing…

A: Given that:¯For the points A2,1,1, B-1,1,-2, C0,-1,0 and D-5,4,6.Let M be the plane containing the…

Q: Find a plane containing the point (6, -4,-3) and the line (t) = +t 270

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Q: Find the line r that passes through the origin and is perpendicular to the TT planes that passes…

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Q: (b) How do you find the distance from a point to a plane?

A: Formula to find the distance from a point (x1 , y1 , z2 ) to the plane Ax+By+Cz+d=0 is given by:

Q: O Find an equation for the plane throught (l,-l,3) parallel to the plane 3x+y+Z=7

A: 1) To find the equation of the plane passing from (1,-1,3) and parallel to the plane  3x+y+z=7

Q: Find the intersection of the following geometric objects: the plane 3x + 2y - z = -9 and the line…

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Q: Which is the fourth point on plane TSW? T. U O Y

A: A plane is a 2-dimensional surface. It can have an infinite number of points. A plane is composed of…

Q: 9. Write an equation of the plane that passes through (2,0, –3) and (a) is perpendicular to the line…

A: Given: The vectors are: a=-1, -2, 3b=3, 0, -2v=2, -5, -4 The equation of plane is, P=2x+y=z+13

Q: Which of the following is the equation of a plane parallel to the yz-coordinate plane and passing…

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Q: ind a plane containing the point Gl,2,-3) and the line of intersection of the pladnes -X+3y -Z E -7…

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Q: Find the equation for the plane through Po(6, – 3,7) perpendicular to the following line. x= 6+t, y…

A: Given equation of the lines are, x=6+t, y=-3-5t, z=5t The given equation of the lines can be written…

Q: The line L(t) = (3+t, 12+5t, -12-5t) intersects the plane 5x - 5y = 15 at what point?

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Q: Which of the following points is on the xz plane? a) (1, -3, 0) b) (0, 4, 0) c) (0, 3, -2) O d) (2,…

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Q: o Find an equahion for the plane throught (l,-l,3) parallel fo the plane 3x ty+Z =7

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Q: nat is

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Q: Determine whether the line x=3t ,y=1+t ,z=2t  and the plane x-y-z= 1 are parallel. If they are…

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Q: Find the equation for the plane through Po(4,9,-7) perpendicular to the following line. x-4+t,…

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Q: O Find an equation for the plane through the point P = (3, −2, 4) that is perpendicular to the line…

A: Given problem:- Find an equation for the plane through the point P = (3, -2, 4) that is…

Q: Q: For the points A(2, 1, 1), B(-1, 1, –2), C(0, –1, 0) and D(-5, 4, 6), let M be the plane…

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Q: Find the equation of the plane with the given description. Contains the lines r1(t) =〈2, 1, 0〉+〈t,…

A: Find the equation of plane containing two lines: r1t=2,1,0+t1, 2, 3 and r2t=2,1,0+t3, 1, 8.…

Q: 5) Given the point Q(2, 0, 1) and a plane p: 3x + y - 4z = 24, Find the distance from Q to p.

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Q: 3. Consider the plane TT: 4x + 3y - 2z + 12 = 0. What is the relationship of the plane to each of…

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Q: Determine the point of intersection, if such a point exists, for the line €: (x, y, z) = (-1,-6, 5)…

A: Given: Equation of line as, l:(x,y,z)=(-1,-6,5)+n(1,3,-2) And the equation of the plane is given as…

Q: d. The plane through P,(2,4,5) perpendicular to the line x=5+t y=1+3t .

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Q: 1. Which of the following points in the standard (x, y) coordinate plane is farthest from the…

A: Which of the following  points in the standard (x, y) coordinate plane is furthest from the origin

Q: Determine the Point OF 3x +y+22 = 45 and the Line witth plaremetre eg dartons 1 = 1+t, y= 3 +2 € ,…

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Q: (2t+l, st-5, lot ) f 4z: Given two lines ( 34, 2++3, zt+1) located in Sice the plane ? plane, find

A: The required equation for the plane is calculating by the below method.

Q: Find the equation of the plane with the given description. Contains the lines r:(t) = (2, 1, 0) +…

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Q: Plot the given points on the Cartesian plane and also find and plot the midpoint. A(H,–T),B(T, U)

A: We have been given - H = 0T = 7U = 0Then,A = H,-T = 0,-7B = T, U = 7, 0Let's draw these points on…

Q: P, Q and R Find a plane that contains S and is parallel to the plane that contains the points

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

Q: c. Find the distance from Po = (3,9, 6) to the plane 3.x + 4y – 5 = 0.

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Q: Given the planes (x, y, z) = (0,0, –3) + s(1,1,–2) + t(-2, –-1,3), and x + y + z + 6 = 0 : a) Are…

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Q: -1. Through (1,5, 2) perpendicular to 37 – J + 4k .

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Q: Y. 14 12 10 8 6 D. --4-2 2. 6 8 10 12 14 A 4. 2. 4.

A: from midpoint formula

Q: Determine the point of intersection, if such a point exists, for the line €: (x, y, z) = (3,– 1, 7)…

A: Given: Parametric equation of line l: (x,y,z)=(3,-1,7)+r(-5,2,1) Equation of plane: 2x+3y+4z=24

Q: Find the distance of point K(1,0,1) to the plane generated by the points P(2,3,1), Q(3,-1,4) and…

A: All options are wrong i am giving Right answer with complete formula and procedure for easy…

Q: Let u = 2 and v = | 0 , and let P = span{u, v}. Find an equation for the plane P.

A: Given: Let xyz be a point in Span {u, v} so there are t, r∈ℝ such that xyz=tu+rv. So,…

Q: Determine whether the planes 2x − z = 1, 4x + y + 8z = 10 are parallel, orthogonal, or neither. If…

A: 2x-z=1,  4x+y+8z=10 Now comparing with a1x+b1y+c1z=d1  &  a2x+b2y+c2z=d2, we get a1=2, b1=0,…

Q: ₁:9x+13y-2z=-4 x = 5+2t y=-5-4t z = 2+3t

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Q: Prove that the perpendicular distance from the point P(xo, Yo, 20) to the plane with equation ar +…

A: Here we use the distance formula between two points.

Q: Find the equation for the line passing through and perpendicular to Hhe plane P= (!,2,-3)…

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Q: Find the intersection of the following geometric objects: the plane 3x - y + z = 3 and the plane 2x…

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Q: x + 4y + 2z = 4, and 4x -3y +4z = 7.

A: Topic - plane and vectors

Q: Consider the plane P, that contains the points A = (1,2, –1), B = (3, 1, 2) and C = (2, – 1, 4). %3D…

A: Equation of a plane passing through three points is given by the formula Therefore  The equation of…

Q: . Find the acute angle between the line joining A(1,2,3) and and the plane containing point…

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