Find an scalar equation of the plane containing the line x = 2 – 4t, y = 4 – 5t and z = 5+t and the point (2, -2, –6).

Q: 5. Determine the equation of the plane that contains the point (0,3,0) and the X = 1 line y = 2t z =…

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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: Find the scalar equation for the plane passing through the point P=(-5, -2, –4) and containing the…

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Q: 4 - x y + 1 %3D 2 1 3 L2 :[x, y, z] = [-2,4,3]+ t[-6, 5, 7], t E F

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Q: Find a scalar equation of the plane x + 2y + 3z = 0 -x+ 3y - 2z = 0 c. 13x + y - 5z = 9 d. 13x+y- 5z…

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Q: Find the trace of the plane 8x – 9y + 2z = -11 in the coordinate xz-plane.

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Q: Find the scalar equation for the plane passing through the point P-(5, 3,-5) and containing the line…

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Q: Find the vector equation for the line of intersection of the planes x + 4y + z = -5 and x + 4z = 0…

A: Here we have to find the vector equation for the line of intersection of the planes x+4y+z = -5 and…

Q: Let y = x² be a parabola in the xy-plane parametrized by r(t) = (t,t², 0). What are the vectors T, N…

A: Solution is given below:

Q: Find the scalar equation for the plane passing through the point P=(4, -5, 3) and containing the…

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Q: Determine a scalar equation for the plane that passes through the point (2, 0, -1) and is…

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Q: For a plane with a normal of n = [1, 2, - 9]   and containing a point P (3, -4, 0), write the…

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Q: Find the vector equation of the line of intersection of the planes x+y+z=1 and x+2y+2z=1.

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Q: Write the scalar equation of the plane with normal vector - [0, – 1, O] and having a y-intercept 3.…

A: Equation of plane

Q: Find an equation of the plane containing the line = 3t, y=2-4t, z = 1+ t and parallel to z-axis.…

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Q: Find the equation of a plane through the point (1, – 1, 6) and orthogonal to the line x(t) = 7 + 4t…

A: Required plane is orthogonal to the given line, say L: x(t)=7+4ty(t)=-3-4tz(t)=-1-6t also, the plane…

Q: Find the scalar equation for the plane passing through the point P=(−4, 2, 10) and containing the…

A: Explained below

Q: Determine the vector equation that represents the curve of intersection between the cylinder 2¹² +…

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Q: Find an equation of the plane. The plane that passes through the point (1, 2, 4) and contains the…

A: Topic = Vector correct answer e

Q: 3. Write the scalar equation for a plane passing through (5,8,-1) and perpendicular to the line x =…

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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: Determine the values of A and C such that the scalar (Cartesian) equation of a plane is  Ax -20y…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: The intersecting curve of two surfaces is given as follows:

Q: Find the scalar equation of the plane that contains the line x+1 -3=. and is parallel to x+2=+4_:+2…

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Q: Find the vector equation for the line of intersection of the planes 2x – 2y – 5z = 5 and 2a + 2z = 1

A: Given  equation of planes 2x-2y-5z=5 2x+2z=1

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: Find a scalar equation for the plane that contains the points P, Q and R

A: We know that equation of plane passing through three points A(x1,y1,z1),B(x2,y2,z2), C(x3,y3,z3)  is…

Q: 4) a) Find the vector parametric equation of the line in R³ that is perpendicular to the plane 2x -…

A: Given plane is, 2x-3y+7z-4=0

Q: Find the vector equation for the line of intersection of the planes 5x + 4y + 5z = 1 and 5z + z = -4…

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Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 5z + 10 =…

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Q: Find parametric equations for the line through the point P(-5,6,7) and perpendicular to the vectors…

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Q: 285. Find the scalar equation of the plane that passes through point P(-1, 2, 1) and is…

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Q: Find a scalar equation of the plane that contains the linex = 1 + t, y = 2 − t, z = 4 − 3tand is…

A: Given,The plane that contains the line x = 1 + t, y = 2 − t, z = 4 − 3t.So, we can say that the…

Q: Find a vector function that represents the curve of intersection of the paraboloid z=7x^2+5y^2 and…

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x² + y²…

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Q: Find the point on the curve of intersection of the paraboloid x² • y² + 2z=4 and the plane x-y+ 2z…

A: This question can be solved by options because we have only two equations and three variables.

Q: Find an equation of the plane through the origin that is parallel to the plane 5x – 4y + 6z + 10 =…

A: Here we have to find the equation of a plane.

Q: Find the scalar equation for the plane passing through the point P-(0,-3, 2) and containing the line…

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Q: Find a vector equation for the curve of intersection of the surfaces x^2 + y^2 = 4 and z = xy.

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Q: Find the points on the hyperboloid 9x^2  - 45y^2 + 5z^2 = 45 where the tangent plane is parallel to…

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Q: Find the scalar equation for the plane passing through the points P1(2, 1, 5), P2(2, 0, 9), and…

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Q: Find a vector function that represents the curve of intersection of the paraboloid z = x^2 + y^2 and…

A: Intersection of paraboloid and cylinder can be obtained by representing y in the form x and z in the…

Q: Find the vector equation of the line of intersection of the planes x+y+z = 1 and x+2y + 2z = 1.

A: The equation of the line vector of the intersection of 2 planes can be calculated using the cross…

Q: Find the value of d in the equation of the plane ax+by+cz+d=0 passing through the point P(3, 1, -2)…

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Q: Find a scalar equation of the plane that passes through the points (1, 1, 1) and (2,0,3) and is…

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Q: Give an equation of the plane whose trace in the yz-plane has equation y = 6z, and in the xy-plane…

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Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 6z + 18 =…

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Q: Find the scalar equation of the plane that passes through point P(−3, 3, 5) and is perpendicular to…

A: To Find: Scalar equation of the plane that passes through point P(−3, 3, 5) and is perpendicular to…

Q: 2. Find the equation of plane which passes through the point (1,2, –3) and the vector i – 2j + 3k is…

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