e equation of a plane is [x, y, z] = [-1, –1, 1] + s[1, 0, 1]+ t[0, 1, 2], s, t, E R. Find the ne.

Q: x-2 Where does the line 3 intersects the xy plane? (5,0,7) O (7,0,5) O (5,0,2) O (0,2,0) O +00 %3D

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Q: Please solve

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Q: 1. Consider the plane 4x – 3y + z = 6. (a) Which of the following points lie in the plane? i. (1,4,…

A: Plane

Q: E. Find the point of intersection of the plane 2x+3y+z 5 and the line x- 3 y+4 z- 1 1 II

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Q: F = (x² – y², y² – 2², z² – x²), S is the part of the plane r + y + z = 1 in the first octant.

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Q: O Find the equ.of Plane that contains p(o,3) and Parallel co the X-2 Plane and PerPendicular to the…

A: We have to find equation of plane with given conditions.

Q: (A) Determine the plane that contain the point A(2,5,1) and the line L, t=x-2, 3t =y-1, t=z+1

A: The equation of the line L given in the parametric form, that is, Thus, the above equation of the…

Q: 2. The plane containing the point P(Xg» Yor Zo) and having the normal vector n = (a, b, c) is…

A: Equation of a plane passing through the point Px0, y0, z0 and perpendicular to the vector n=a, b, c…

Q: Let T, denote the plane parallel to the xz-plane through the point (1, 2, 3). Let n2 denote the…

A: To solve this problem first of we find the equation of the plane π1 and π2 in standard form and then…

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: Let A(1, 2, 1), B(3, 1, 2) and C(2, 1, 2) be points in R³. a) Find the point-normal form of the…

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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: ind the equation of the plane passing through the three points A = (-1,0, 2), B = (2, –1,2), C = (3,…

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Q: Which of the following describes a plane perpendicular to the vector n = (2, 1, -4) and contains the…

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Q: Let P be the plane R3 with equation x+y-2z=4. the origin (0,0,0) is not in P! find two vectors in P0…

A: Given  x+y-2 z=4      .....(1)

Q: 5. x=4-s+t Find a vector perpendicular to the plane = y = 1+ s-t (z=1+s+t b) [5, 5, 0] a) [1, -3,…

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Q: 9. (a) Find the vector form r(t) = rõ + tỡ of the line through the points P(2, 7, 5) and Q(7,8, 12)…

A: a) A point on vector is P(2,7,5) so, Answer(a):

Q: · Let A the area of the triangle ABC is given by ("1, ул), В %3D (x2, Y2), and C = (x3, y3) be…

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Q: Let r() = (In1, 1, 5). Find the equation of the osculating plane corresponding to1 = 1.

A: Find the point at t=1 the vector r(t)=lnt,t,t22 corresponds. lnt,t,t22=ln1,1,122=0,1,12=0,1,0.5…

Q: Show that the vector form (x, y, z) = (-5, 1,0) + t(3,2, 1) for some parameter t ER satisfies the…

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Q: Given vector R(x, y, z) = (3,4, –4), obtain (a) a unit vector Ŝ that lies in the x-y plane and is…

A: The given vector is Rx,y,z=3,4,-4. (a). We know that two vectors in ℝ3 plane are perpendicular to…

Q: Find the equation of the plane E passing through the point P(2,3,1) and parallel to the vectors K =…

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Q: ind the equ.of Plane that Contains plos1,3) and Parallel to the X-2 Plane and PerPendicular to the…

A: Solution:-

Q: The equations for the plane through p0(0,2,-1) normal to n =3i - 2j - k O 3x-3y-3z=0 O 3x-3y=z O…

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Q: Consider a plane II whose unit normal vector pointing outward from the origin is n = ai+ bj+ck and…

A: Projection of any vector x,y,z on the plane along the normal vector a,b,c will be d.

Q: Find the barycentric coordinates of p with respect to the affinely independent set of points that…

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Q: The equation of the plane that passes through the point P(1,0,0) and has the vector n = (0,0, 1) as…

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Q: 2. Which of the following describes a different plane than the other three? (a) x + 2y + 3z = 6 (b)…

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Q: Let P be the plane with equation x-2y-2z = -11. Find four distinct points on P at distance 6√2 to…

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Q: E. Find an equation of the plane passing through the point (6, 3, 5) and containing the line of…

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Q: -) Find the vector form F(t) = ro + tu of the line through the points P(2, 7, 5) and Q(7,8, 12) Find…

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Q: a) Show that the line I = 0, y =t, :=t where teR a) lies in the plane 6r+4y-4r = 0 b) is parallel to…

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Q: The z-coordinate of the point of intersection of the plane r+2y +z= 6 and the line through the…

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Q: At which point does the line described in question 3 intersect the plane described above? (Hint: You…

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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) 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;…

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Q: a) Find the equation of the plane which passes through the line of intersection of the planes 4x –…

A: Both parts of questions are solved in each steps.

Q: t u - (1,1, -2) аnd v = (a, –1, 2). For what values of a are u and v orthogonal?

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Q: Let k ER and consider the plane T in R3 with vector equation X1 1 X2 k + s + t -1 s, t E R. X3 It is…

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Q: 1. Show that A(r - ro) + B(y - yo) =0 is an equation for the line in the ry-plane through the point…

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Q: Curve In Exercise 56, sketch the plane curve and find its length over the given interval.  56. r(t)…

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Q: c) Find an equation of the plane that contains the line L: 1=1-t, y = 2+t, z = -3t where teR and the…

A: Equation of plane that contains the line x=1-t, y=2+t, z=-3t where t is in R and the point…

Q: An equation of the plane passing through the points A(-1;2; 0),B(0;1;2) and C(1; –1;0) is: O…

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Q: ind an equation for the plane that passes through the point A(1,2,3)parallel to u = 2i + 3 j + k nd…

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Q: Which one of the following equations describes the plane passing through the points (1, 1, 0), (0,…

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Q: (a) Let P be the plane in R3 defined by the equation n•r = d, where |n| = 1. Prove that |d| equals…

A: Suppose general equation of plane is ax+by+cz=d .The distance from point α,β,γ to required plane is…