Find the angle between the plane z=0 and the plane passing through the points (0, 0, 0), (3, 1, 0), and (0,3,2) correctly in rad. _________radians.

Q: Perform a rotation of axes to eliminate the xy-term. (Use x2 and y2 for the rotated coordinates.)…

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Q: Find the parametric equations of the line that goes through the point P(−2, 0, 5) and is parallel to…

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Q: Let P = (2, 1, 3), Q = (-3, 5, 1), and R = (1,0, 4) be poits in R°. Let a = PQ and b = PR, as usual.…

A: Hi !! Thank you for the question. Since, there are multiple parts in the question, we will be…

Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

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Q: Question # 4: Let and y = For what value(s) of h, is y in the plane generated by vi and va?

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Q: Question 25 etermine the coordinates of the foci given the standard equation - 3) (y+2) = 1 %3D 169…

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Q: (a) Find the cosine of the angle between the lines L1 and L2 whose vector equations are given below:…

A: (a) The directional vector of the line L1 is n→1=1, 2, 3 and the directional vector of the line L2…

Q: Part A Find the parametric equations of the line of intersection of the following planes: T1: 5x +…

A: Find the point of parametric equation of the line of intersection, and angle between two planes

Q: 14. State whether the following pairs of planes intersect. If the planes intersect, determine the…

A: Two planes are given by, π1: x-y+z-2 = 0  and π2: 2x+y+z-4 = 0. The objective is to check whether…

Q: 12. Find the parametric equations of the line that contains the point P and intersects the line L at…

A: Given equation of the line is  L:x=-2+2t , y=4+2t , z=2+t          Then, the co-ordinate of any…

Q: 11. Given that lines r (i+ 2j + k) + t(i + 2k + 2k); r= (6i+ 6j + 6k) – s (5i + 4j + 5k) find a) The…

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Q: Find parametric equations for the line that passes through the points P and Q. P(1, –2, 3), Q(5, 1,…

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Q: 2. By definition, the angle of intersection of the two curves is the angle between the two tangent…

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Q: Which vector from the choices given below is tangent to the curve at the point (1, 1, 1) ti +ri +…

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Q: Find parametric equations for the line through P = (4, 0, 3) and Q = (3, 5, −5). Use them to find…

A: Given P (4,0,3) and Q (3,5,-5) So, r0=4,0,3 v=3,5,-5-4,0,3  =-1,5,-8 The parametric equation is…

Q: 5. The coordinates of the points A, B and C, are (0, 1, 3), (-1, 0, 1) and (1, -1, 2) respectively.…

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Q: the Complex Sketch plane the curve in given by. i) z' + z? -2.

A: The solution is as follows below :

Q: The rotation R : R? → R? around the origin anticlockwise by the angle 0.

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Q: Find the parametric equation of the line through the point ?(3,−2,1) parallel to the line ?=2−2?,…

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Q: II. Grafique el punto cuyas coordenadas polares están dadas. Luego, determine las coordenadas…

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Q: i. the normal vector to the plane ABC. ii. the parametric equation of the line perpendicular to the…

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Q: a) Interpret the parametric equations     x = x1+(x2-x1)t     y = y+(y2-y1)t where 0<= t <=1, which…

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Q: Q1) (a) Find the parametric equations of the line L that passes through (3, −2, 1) and is…

A: we need to find  the parametric equations of the line L that passes through (3,-2,1) and is…

Q: Find the parametric equations of the line of intersection of the planes, and find the angle between…

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Q: Find parametric equations for the line that passes through the point P and is parallel to the vector…

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Q: Part b: ( a) Find the parametric equation of the line that passes by P(1, 2, 2) and that is parallel…

A: as per company guidelines we solve only first question when multiple question being posted.

Q: (c) Let u(r, y) be the harmonic function in the disk B %3D

A: Given, u(x, y) be the harmonic function in the disk…

Q: Find parametric equations for the line that passes through the point P and is parallel to the vector…

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Q: 3. What is the parametric equation for the line through the point (1 ,2, 3) parallel to the x- axis?…

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Q: The equation of a line is r=i- 3j + 7k + µ(3i + j+ 2k)and th= equation of a plane is 2x + 3y – 2z =…

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Q: The image im(A) is a plane in R* passing the origin. Find the distance from the vector b to the…

A: First, we will find the basis of im(A) for…

Q: State whether the following pairs of planes intersect. If the planes intersect, determine the…

A: Given: The equation of two planes are: V1 : x − y + z − 2 = 0, V2 : 2x + y + z − 4 = 0

Q: Transform pentagon BEARS according to (x, y) → (x +6,y+B). Write the coordinates for pentagon…

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Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis.…

A: Component form of v is ( vx , vy ) . Here vx = || v || cos A  , vy = ||v|| sin A And A is angle with…

Q: Find parametric equations for the line that passes through the points P and Q. (Enter your answers…

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Q: (a) Construct the image of the point A under the composition of ƒ =ref (the reflection with respect…

A: As per the question we have to construct the image of the given point A , after being reflected by…

Q: 65. Find parametric equations for the line through the point (0, 1, 2) that is parallel to the plane…

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Q: 3. What is the parametric equation for the line through the point (1,2,3) parallel to the y - axis?…

A: The solution is given as follows

Q: 6) Find parametric equations for the line through P(0, -2,-2) and Q(1,1,0).

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Q: Let Q(t)= t i + t-1 j. a) draw the vectors Q(1), Q(2), Q(3), Q(4), and Q(5). b) Add a sketch of the…

A: Part (a)Please see the table below and the plot on the white boardtQ(t)= ti + t-1j.xy1Q(1) = i +…

Q: Determine the XY-coordinates of the given point if the coordinate axes are rotated through the…

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Q: Rotate the xy-axes in the plane counterclockwise through an angle θ= 135° to obtain new x' y' -axes.…

A: Given Data The angle of rotation in anticlockwise direction is θ=135°. (a) The expression for the x’…

Q: Q5) Find the angle between the plane x+y-z=3 and the plane that perpendicular to the line has the…

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Q: B Find the parametric equation of the plane passes through the point (-3,0,7) and perpendicular to…

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Q: Find the angle of intersection of the plane -2x – 3y – 5z = -4 with the plane 5x + 5y + 4z = -5.…

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Q: 6) Find the following: a) An equation of the plane passing through the points P(2,1, 10, Q(-1, -1,…

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Q: A line given by the parametric equations x 2+3t, y 1+t, z 5+4t, forteR Which of the following is an…

A: Use for mula to calculate

Q: His a point in the Catesia Plane Delteiraine 11) OB 2) Cos B 113) CosecB 1 tan B

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Q: Complete the parametric equations of the line through the point (8,6,-2) and perpendicular to the…

A: equation of line passing passing through the point 8,6,-2 and perpendicular to the plane , x-7y-z=-3