a) Check that the line r: (x, y, z) = (1,0,1) + t(1, –1,0) is parallel to the plane n:x + y +z = 0; %3D

Q: 25. Find the intersection of the line [x, y, z] 2х — 4у + 7z —26 %3D 0. [1,4, – 2] + t[1, – 1,3] and…

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Q: Find the equetion of the plane contains the line x=3t,y=1+t, z=2t, and parallel to the line of…

A: Equation of linex=3+ , y=1+t , z=2tIn carterian formx-03=y-11=z-02Line passing through 0,1,0 and…

Q: Where does the line x = 2−t, y = 3t, z = −1 + 2t intersect the plane 2y + 3z = 6?

A: Where does the line x = 2−t, y = 3t, z = −1 + 2t intersect the plane 2y + 3z = 6? Given x, y, z in…

Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the plane through U, V, and W, expressed in…

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Q: Find the intersections of the line x = -2, y = 4 + 2t, z = -3 + t with the xy-plane, the xz-plane,…

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Q: Find the intersection of the line and the plane. x + y + z = 14, r(t) =〈1, 1, 0〉+ t〈0, 2, 4〉

A: Given that, The equation of the line is: x + y + z = 14 And, the equation of the plane is:  r(t)…

Q: Find a plane through P (2, 1, 1) and perpendicular to the line of intersec- tion of the planes:…

A: find a plane through P2,1,1 and perpendicular to the line of intersection of the planes  2x+y-z=3 ,…

Q: 4. (a) Show that the line l given by l: 1= 2+3t, y=1+4t, z= 5+ 2t, te R, lies in the plane II given…

A: Given problem:- Show that the line  given by   l : x = 2 + 3t , y = 1 + 4t , z=5+2t ,t in R   lies…

Q: Determine whether the plane x + y + z = 9 and the line x = t, y = t + 1, z = t + 2 are parallel,…

A: Given: The planes x + y + z = 9 and the line x = t, y = t + 1 , z = t + 2.   To determine Whether…

Q: Evaluate (x2 + y? + z)dS, where S is the portion of the plane z = x + 2 that lies inside the…

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Q: 3. Find the plane determined by the intersecting lines L: x = -1+t, y = 2+t, z = 1- t; L2: x = 1 -…

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

Q: Find the distance of point A(1,0,2) to the plane 3x+y+z=9?

A: Here we have to find the distance from the point A(1,0,2) to the plane 3x+y+z-9=0

Q: Find the point at which the line intersects the given plane. x = 2 − 2t,    y = 3t,    z = 1 + t;…

A: Given that  x = 2 − 2t,    y = 3t,    z = 1 + t;    x + 2y − z = 4 first we will substitute values…

Q: Find the plane containing the intersecting lines L1: x = -1+t, y= 2+t, z = 1 – t; L2: x = 1 – 4s,…

A: The given intersecting lines are  L1: x=-1+t,y=2+t,z=1-t; -∞<t<∞L2: x=1-4s,y=1+2s,z=2-2s;…

Q: Find the distance between the parallel planes. x + y + z = 1 and x + y + z = 3

A: The distance between two parallel planes is the shortest distance between their surfaces. Distance…

Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y +z = 1 that lies above the…

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Q: 24. The plane that contains the line x = 1 + t, y = 2 – t, z = 4 – 3t and is parallel to the plane…

A: To find out equation of plane first we change the equation of line in symmetrical form then find out…

Q: For what positive value of cc is the acute angle between the plane containing the points A(0,0,1),…

A: According to the given information, it is required to find the positive value of c is the acute…

Q: Find the point where the given line intersects the given plane x = 1-t, y = t, z = 1+t, z = 1- 2x +y

A: Given lines, x=1-t , y=t  , z=1+t  Given plane, z=1-2x+y To find the point where the given line…

Q: Determine whether the plane x + y + z = 9 and the line x = t, y = -2t + 1, z = t + 2 are parallel,…

A: The given equation of line is in parametric form, x=ty=-2tz=t+2 Convert it into the cartesian form,…

Q: 2. Find the plane that is orthogonal to the line : +1 = 431 = z and contains the point where l…

A: line parallel to the vector  V=⟨a,b,c⟩ passing through the point (x1,y1,z1) is given by the…

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: 25. Determine the distance between the parallel line {y = 5-t, te R and the plane {y = 2-s -t, s,t E…

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Q: 2. Do the three planes x + 2y + z = 4, y - z = 1, x+ 3y= 0 have at least one commom point of…

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Q: The distance from the point P(1,2,3) to the plane x +y + z = 0 is

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Q: Find the equation of the plane that contains point P(1, -1, 2) and has the normol n= 2¿+3j+Sk.

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Q: Is the line x = 4+ 2t , y =-t , z = -4t – 1 parallel to the plane 3x + 2y + z = 7? %3D

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

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Q: Find the point at which the line intersects the given plane. x = 4 – 4t, y = 5t, z = 1 + t; 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: Find the trace of the plane in the given coordinate plane. Зх — 9у + 82 %3D7, yz

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Q: Find the intersection of the line r(t) = 3t + 2, 1, −7t and the plane 2x − 3y + z = 5.

A: r(t)=3t+2, 1, -7t and the plane 2x-3y+z=5

Q: Show that the line x = −1 + t, y = 3 + 2t, z = −t and the plane 2x −2y−2z + 3 = 0 are parallel, and…

A: Here we have to show that the given line,  x=-1+t, y=3+2z, z=-t and plane 2x-2y-2z+3=0 are parallel…

Q: Find the distance from the point B = (1, 0, 2) to the plane P whose general equation is x + y -z =…

A: Equation of the plane is Given point is

Q: Find the intersection of the line and plane: 4x + 4y – 3z = 5, r(t) = (1, 1, 1) + t(1, –2, 3) %3D…

A: Given that line and plane are 4x+4y-3z=5  ,rt=1,1,1+t1,-2,3To find :intersection point of line and…

Q: A. Show that the planes (x+ y– z = 1 ) and (2x – 3y+ 4z = 5 ) are neither parallel nor…

A: let the normal vectors for the vectors be a1, a2 thus a1=<1,1,-1> and a2=<2,-3,4>. Let…

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: 2. Do the three planes X + 2y + z = 4, y - z = 1, x+ 3y = 0 have at least one commom point of…

A: The equation of the plane is given by the formula ax+by+cz+d=0. The system of planes can be solved…

Q: // 2° zdS, where S is the part of the plane z = 4+ 2æ + y above the rectangle [0, 5] × [0, 3]…

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Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y + z = 1 that lies above the…

A: Surface integral

Q: 02. A. Show that the plane 3x + y - z = 9 and the line {x = 2,y = -1+ 3t ,z = 1+ 3t} are parallel,…

A:

Q: a) Show that the line I = 0, y = t, z =t where te R a) lies in the plane 6z+4y–4x = 0 b) is parallel…

A: In the question it is asked to solve for the planes having equation given below.

Q: Find a plane that contains S and is perpendicular to the plane that contains the points

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Q: Show that line y+1 is parallel to plane x- 2y + z = 6 С.

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Q: What is the intersection of the plane x+2y+z=0 and the line (x,y,z) = (0,1,2)+ k(-1,1,2), kER?…

A: hello greetings from bartelby.i am here to help you.

Q: Show that a indeed perojective plane of gives 0rder BİBD (n+n+,n+),!

A: We need to prove that a projective plane of order n indeed gives a BIBD (n2+n+1, n+1, 1)

Q: What is the equation of a plane whose r-intercept is a, y-intercept is b, and z-intercept is c?…

A: Solve for the equation

Q: Find the point on the plane 2x + 5y + z =9 that is nearest to (2,0,1). Vhat are the values of x, y,…

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Q: Find the point of intersection between the planes TT :x+y-z =1, n, : 2x – 3y -9z = 10 and n, : x +…

A: The three planes are, π1=x+y-z=1 π2=2x-3y-9z=10 π3=x+2y-3z=-4

Q: ind the point at which the line intersects the given plane. x = 4 – 4t, y = 5t, z = 1 + t; x + 2y –…

A: