[] -3 -3 Let y = -9 uj -5 u2 5 Find the distance from y to the plane in R3 spanned by ul and u2.

Q: 12 3. 5. 13 18 -1 For what value of hs in the plane spanned by j and i? Preview Answers Submit…

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Q: 2. Give the symmetric equations of the line l perpendicular to the plane T : 5x– 2y = z+4 and…

A: we have to find equation of line.

Q: = - 1+ 3t Find a plane through the point (7,5,-5) and orthogonal to the line y(t) = – 6 – 3t z(t) =…

A: The given line is: x+13=y+6-3=z-4-2

Q: Find a function r(t) that describes the line through P(3,4,5) that is orthogonal to the plane 2x-z=4

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Q: 9. Find the equations of the planes that are parallel to 2.x - 2y + z = 5 such that the distance…

A: We will solve the problem.

Q: (1) Find an equation for the plane that passes through the point (–1,2,2) and contains the line of…

A: Given: Equation of planes x+y-z=5⇒x+y-z-5=0 and 3x-y+5z=3⇒3x-y+5z-3=0 and point -1,2,2, To find: The…

Q: Let L be a line which passes through the point (-4,0, 1) and is perpendicular to the plane x + 2y +…

A: Please refer the attached image for complete solution.

Q: 2 4. Let Li be the line x = + s 1 and let L2 be the line x = +t|-1 a Find the point of intersection…

A: Equation of plane contain point (x1,y1,z1)  and Normal vector Direction cosine <A,B,C>…

Q: Example 8: Find the point where the line 2t, and z = -3t intersects the plane x = 1 + t, y = –…

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Q: 5 3 - 2 Let y = 1 Find the distance from y to the plane in R° spanned by u, and uz. -2

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Q: (24 17. 3417.4) %3D Find the equation of the plane that contains the line x = 3t, y = 6 - t, z = 4…

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Q: -5 3 Let aj = 3 a2 = -8 |, and b = -5 For wha -1 2 h value(s) of h is b in the plane spanned by aj…

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Q: B. Sketch these Cartesian products on the x-y plane R² (or R for the last two). 9. {1,2,3} x…

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Q: What kind of conic section is given by the quadratic form ? -11x,2 + 84x,x2 + 24x,2 = 156 Transform…

A: Given Quadratic Equation is, -11x12+84x1x2+24x22=156 Matrix Representation form is, A=-11424224 Find…

Q: At what point does the line r = (6 – 3t)i +(-2+2t)j+(-1– 3t)k intersect the yz –plane. Select one: О…

A: When the line intersects the plane yz the value of the x coordinate is zero. Hence the solution of…

Q: The equation of the plane passing through A(2,1, – 1), B (0, –2,0), and C(1,-1,2) is: O 2x+y-z=0…

A: solve the following

Q: 45. Find the distance from the plane x + 2y + 6z = 1 to the plane x + 2y + 6z = 10.

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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: 3. Evaluate ff(+2y- )dS where S is the portion of z = 5= 2y + that lies over the triangle in the…

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Q: find the trace of the plane in the given coordinate plane.  3x + 4z = −2, xy

A: To find the trace of the plane in the given coordinate plane  3x+4z=-2 --- (1) in the xy plane

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: 3 find +he equation of Hhe plane perpendicul av bo the plane x+24+5z=|| and passing through the…

A: The given plane is,

Q: Find the symmetric equations of the L that is parallel to the two planes x+y-z= 2 and z + 3y+ z =…

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Q: Given: a plane containing the point P(-2, 5, -3) and the line [x, y, z] = [-1,2,5] + s[3, –4,1]…

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Q: Let L be a line which passes through the point (-8, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Evaluate Sf,(z+ 3y – x²) dS where S is the portion of z = 2 – 3y + x² that lies over the triangle in…

A: Ans :

Q: 9. Find the equation of the plane through P(1,1,4) that is parallel to the plane x+ 5y – z + 8 = 0

A: The scalar equation of parallel planes differ only by a constant Therefore, equation of the required…

Q: 1. Find the equation of the plane that passes through the points P(2,0,1), Q(1,0,-1) and R(3,0,1).

A: We have, Vectors in the plane are, Therefore, equation of plane passes through 3 points will be,…

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: 1. Find the distance between the two planes - 2y + z=4 and z-2y+ :-1 HI

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Q: 4 k V1 = V2 = -5 ; y= -6 -2 k For what value(s) of k is y in the plane spanned by vị and v2?

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Q: Among all the points on the graph of z = 10-x2 -y² that lie above the plane r+2y+3z = 0, ind the…

A: Given that z=10-x2-y2 and x+2y+3z=0 Find the point which is farthest from the plane.

Q: 19. Which plane of the followings passes through the origin? x-4y+5z+1/2 =0 2x+3y+7z=0 4x+2y+6z=1 O…

A: If plane passing through origin  then constant value in the equation of the plane is zero.

Q: Find the symmetric equations of the L that is parallel to the two planes x + 2y - z= 2 and x + 6y+ z…

A: Given: Two planes, P1: x+2y-z=2, P2: x+6y+z=-3, Point P1, 2, 3

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: Determine the value of kk so that these planes in R^3: 3kx+y−5kz=-10 2x−3y+z=−12 are orthogonal.…

A: Given: The planes 3kx+y−5kz=-10 and 2x−3y+z=−12 are orthogonal.

Q: 4. y=4-x² , y=3x and the x-y plane is given by the fol expresions.

A: We have to choose the correct option according to the given information

Q: Let L be a line which passes through the point (-7,0, 1) and is perpendicular to the plane x + 2y +…

A: Here we find the equation of line L and also find the intersecting point of line and plane.

Q: Find the eguation f Plane that Passes through P(12-1,3) and s Parallel to the Plane 3X++6? ans. 3X+y…

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Q: Find the plane determined L1: x=-1+t 12: x=1-4s by the intersecting lines: y=2+t y=1+2s 2=1-1-3-1-00…

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Q: Q3: Let L be the line of intersection of the planes 3x + y -z = 4 and 5x + y + 2z = 1 Find the plane…

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Q: Which of these planes pass through the origin? Зх — 5у+ 2z 30 5х — 3 %3D 0 = 4х + у %3D 0 — 4х — 5у…

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Q: 3 Find the e qu.of Plane that Contains elol; 3) and Parallel to the X-2 Plane and PerPendicular to…

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Q: -:Q1 Evaluate , (x- 2y) dA, where R is the parallelogram in the xy-plane with vertices (0,0), (4,1),…

A: The objective is to evaluate ∫∫Rx-2ydA where R is the parallelogram in the xy plane with vertices…

Q: 16. Find an equation of the plane through the point (1, 1, –2) and parallel to the plane 3r – z =

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Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: 6.) Consider the points P(-1,2,5), Q(2, –3, 0) and (i) Write an equation of the plane containing t

A: Equation of plane: We know that, the equation of plane that passes through point (x, y, z) is given…