calc 3 make sure its right please Find a parametric representation for the plane that passes through the point (-1, -3, -2) and contains the vectors i + j - k and i - j + k. x = y = z = -2 - u + v

Q: 6. Write vector and parametric equations of the plane. a) parallel to the xz-plane and through the…

A:

Q: The Cartesian coordinates of a point in the xy plane are (x, y) polar coordinates of this point.…

A: We know that, a cartesian co-ordinate x,y can be converted into polar co-ordinate r,θ as r=x2+y2…

Q: 90. a. Determine the vector and parametric equations of the plane that passes through the points…

A:

Q: Lucas does not like Dustin weapon and decides to design his own. His model has a plane that contains…

A:

Q: O Represent the parabola 4=2文+1 by a vector valued funchion and sketch it (show everything !)

A: A parabola is a conic section. When a plane parallel to another plane and tangential to a right…

Q: a line is parallel to the vector i+ 5j+3k and passes through the point P = (6, 2, 4), then the…

A:

Q: 1. Determine vector and parametric equations of the plane that contains the points A(1, 2, -1), B(2,…

A: Since you have posted multiple questions. we will solve first question only due to the bartleby…

Q: (A) Find the parametric equations for the line through the point P = (-5, 0, -3) that is…

A: Equation of line.

Q: 3. Quadrilateral ABCD with vertices A(0, 6), B(-3, -6), C(-9,-6), and D(-12, -3): a) dilation with…

A: Given: Quadrilateral ABCD with vertices A(0, 6), B(-3, -6), C(-9, -6) and D(-12,-3) (a) Dilation…

Q: Consider the plane that goes through the point (4, 1, 3) and is orthogonal to vector (2, 3, 1). Find…

A:

Q: Find the parametric form of the equation of the line passing through the point Po(-2,-1,3) and…

A:

Q: a) Write parametric equations for the plane in Rº that passes through the point (2, 3, 1) and is…

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: (a) Find a vector parallel to the line of intersection of the planes 4x + 3y – 2z = -5 and -5x + y –…

A:

Q: 5. Find all vectors such that x v = . 6. Find parametric equations for the line through (2,4,-2)…

A: (6) Given :- The parametric equations for the line through 2,4,-2 that is perpendicular to plane x…

Q: Find parametric equations of the line perpendicular to the yz-plane passing through the point (-3,…

A: We have to find the x ,y,z

Q: Find the parametric equations of the intersection of the planes x + (y - 3) + z = 0 and -x + (y + 3)…

A:

Q: 2. (a) With reference to a Cartesian coordinate system 0xyz, find the plane that contains the points…

A: Position vector of points, A→2,1,3 ; B→3,0,2 ; C→-1,1,4The position vectors are relative to…

Q: 3. Does the parametric equation r = (2,-5,2) + s(1,4,2)+(-2,-3,1), s,/€ R, and the vector equation…

A:

Q: Find a set of parametric equations for the line passing through the point (2, 0, 7) that is parallel…

A: The objective is to find a set of parametric equations for the line passing through the point 2,0,7…

Q: Find parametric equations of the line through Po(xo, yo, Zo) parallel to v. 4 (а) Ро(3, 4, —2), v…

A: a) A line is passing through the point P03, 4, -2 and parallel to the vector v→=4i^-5j^+2k^. The…

Q: a)A PARAMETRIC form equation of a plane whose cartesian/normal form equation is: 2x – 3y – 4z + 10 =…

A: The parametric form of a plane is given by the standard form . The cartesian form of the equation of…

Q: Consider the points A(2, –1,3), B(7,0,5) and C(0, 1, 7), and the line l with symmetric equations x –…

A: Here we can use following formula  AB→=B-A Angle between two vectors a→ and b→ is…

Q: ion cannot exist for a plane. 4. Determine the vector, parametric, and symmetric equations of the…

A: In this question, we want to find the vector, parametric and symmetric equations of the line Passing…

Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Here we find the vector and parametric equations of line.

Q: (a) Find a vector parallel to the line of intersection of the planes 3x – 2y + 4z = -3 and За — 4у +…

A:

Q: Find a set of parametric equations for the line passing through the point  (2, 0, 5)  that is…

A:

Q: 3. Find an equation of the plane passing through the points (1, 2, -6), (2, 3, -2), and (-1, 4, 8).…

A:

Q: 3. Determine vector and parametric equations for the plane through the point (1, -2, 3) and parallel…

A: Here we are given a point and perpendicular direction. We will express equation of plane in vector…

Q: Find a set of parametric equations of the line with the given characteristics. The line passes…

A: We have to find a set of parametric equations of the line with the given characteristicsThe line…

Q: A line passes through the points P(-9,5, - 1) and Q(10,1,2). Find the standard parametric equations…

A: Solve by using parametric equation of line

Q: (a) Find a vector parallel to the line of intersection of the planes 2x + 5y + 2z = -9 and x y – 2z…

A:

Q: A plane contains the point B(-3, 2, -4) and the line with parametric equations x= 1 + 2?, y = −t, z=…

A: Explanation of the answer is as follows

Q: Determine the scalar, vector and parametric equations of the plane that passes through the points…

A:

Q: A line passes through the point (8, - 5,7), and is parallel to the vector 9i + 7j + 10k. Find the…

A:

Q: Find a set of parametric equations for the line passing through the point (2, 0, 4) that is parallel…

A: To find a set of parametric equations for the line passing through the point 2, 0, 4 that is…

Q: Find an equation of the plane. The plane through the point (3, 2, 3) and with normal vector 9i + j…

A: Consider the provided question,

Q: Give a vector parametric equation for the line through the point (1,2) that is perpendicular to the…

A: Here ,       given line -3-3t,3-2t    we gave to find the vector parametric equation for the line…

Q: b) Find parametric equations of the plane (P) containing the point P(1,-2, 0) and the vectors û and…

A:

Q: 1. Let L be the line through (2, 5) and parallel to v = (3, -1). (a) Parametric equations of L are y…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Parameterize the plane that contains the three points (−1,3,2), (12,12,−8), and (30,15,40).…

A: The given points are: (-1, 3, 2),  (12, 12, -8),   (30, 15, 40)

Q: Consider the points A(2, -1, 3), B(7,0, 5) and C(0, 1, 7), and the line with symmetric equations…

A: We will use vector properties and equations of line and plane to solve all part  Note : I have…

Q: Complete the parametric equations of the line through the point (5,-7,-8] and perpendicular to the…

A:

Q: A. Consider the plane with direction vectors à = (8,-5,4) and b = (1,-3,-2) through P(3,7,0). 1.…

A: We need to solve plane problem.

Q: 11. A plane has 3x + 2yz + 6 = 0 as its Cartesian equation. Determine the vector and parametric…

A: This question can be solved using the concept of planes in three dimensional geometry.

Q: A) find a vector parallel to the line of intersection of the planes -3x - 2y - 2z = -1 and -4x - 2y…

A: Equation of line of intersection

Q: Consider the points A(2, –1,3), B(7,0,5) and C(0, 1, 7), and the line l with symmetric equations х —…

A: We have to solve given Questions

Q: Find parametric equations for the lines The line through (2, 4, 5) perpendicular to the plane 3x +…

A: 1) To find the parametric equations for the lines. The required line is perpendicular to the plane…

Q: 6. Find a parametric representation of the line of intersection of the two given planes. 2x+ y- z= 6…

A:

Q: 3. The position vector [3 2 1 1] lies in the YZ plane and forms 30 degree with the principal axis.…

A: Given: Position vector 3211 lies in the YZ plane and forms 30°. To find: On rotation, it forms 45°…

Q: Find an equation of the plane passing through (0, - 2,3) that is orthogonal to the planes 2x + 2y -…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.