19. Find the equation of additional variables and the equation of symmetry for the line passing through the following points. (1) Through the points (-1,3,-2) and the points (6,3,-1)

Q: vector furm : r(t) = ro

A: To represents the equation of line in space ,  The coordinates are  x0, y0 ,x1,y1. a. To represent…

Q: The point P(4, 1) lies on the curve y = Vx - 3. (a) If Q is the point (x, Vx - 3), use your…

A: Given Point P =4,1 which lies on the curve y=x-3

Q: Using vector methods, prove directly that if two sides of a quadrilateral are parallel and equal in…

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: ines in 2d: Determine the parametric, vector and scalar equations for line passing through (-2,11)…

A: Given :            to find parametric equations through a point (-2,11) and (6,1)…

Q: Vector Calculus Given, A = 2? zi – 2y32j+ x} zk. Find divA at the point (1, –1, 1).

A:

Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, -1, 4),…

A:

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A:

Q: 4. Identify the component form of the vector that maps AABC to its image AA'B'C' A. B. 2 C. D.…

A: Given graphs  1) vector that maps  triangle ABC has vertices A(3,-1),B(7,-3),C(1,-6) to its image…

Q: vector (A) = -2 i-5j +2 k vector (B) = -5 i-2j-3 k Find the magnitude of (vector A. vector B)

A:

Q: Zero component of the curl For what vectors n is(curl F) ⋅ n = 0 when F = ⟨y, -2z, -x⟩?

A:

Q: Find Vector, Parametric and Scalar equations for the line that passes through t -2,11) and (6,1).

A: Given: - The line that passes through the points -2,11and 6,1. To find: - The parametric equations…

Q: 2. A triangle is formed by the points P = (1,0, 3), Q=(4,-1, 3), and R = (6, 1, -2). (a) Sketch the…

A:

Q: Transforming vector filed in Cartician coordinate to Cylindrical coordinate, how to find its…

A:

Q: We define a median vector of a triangle to be the vector from a vertex of the triangle to the…

A: Let ,The triangle be ∆ABC A(x1, y1, z1)B(x2, y2, z2)C(x3, y3, z3)AM→ , BM→ , CM→ be the medians

Q: Topic : (VECTOR AND THREE-DIMENSIONAL ANALYTIC GEOMETRY)

A:

Q: 4. This question is about dot products and normal forms. (a) Give an interesting example of a…

A: (a) An interesting example of a hyperplane H in  in normal form isH: 3x+2y−5z=7In this example, the…

Q: find a vector equation and parametric equations and symmetric equation containing (a,b,c) parallel…

A: To find the vector equation, parametric equation and symmetric equation containing the point (a,b,c)…

Q: Topic: Vectors and Geometry of Space → identify and sketch the following item. identify its traces…

A: The general equation of the elliptic cone is given by z2=x2a2+y2b2   The general equation of a…

Q: Describe and compare the solution sets of x, + 7x, - 6x3 =0 and x, + 7x2 - 6x3 = - 4. ..... X1…

A: To describe and compare the solution sets of below two equations. x1+7x2−6x3=0x1+7x2−6x3=−4

Q: Triangle ABC has points A(-1,2), B (0, -3) and C (1, 2). A translation of this triangle results in…

A: Observing from the given point we conclude that

Q: Dot Product Find the dot product of the vectors a = (1, 3, −4) and b = (–2,3,1)

A:

Q: Topic : (VECTOR AND THREE-DIMENSIONAL ANALYTIC GEOMETRY)

A:

Q: 1. (Vector Operations) Consider = and = k. (a) Find a unit vector in the opposite direction as a.…

A: Answer given below.

Q: Without giving a numeric example, explain using the LEAST number of words the steps needed to…

A: The vector equation of a plane in normal form is   r.n^=d Here r is the position vector of a point…

Q: Let the space curve be the intersection of two surfaces z = x² + y² and y² + z² = 1. Draw this curve…

A: As per the question we are given two 3d surfaces defined by the equations : z = x2 + y2   ;   y2 +…

Q: Can you give me an example (with problem, solution, and a detailed description of the process that…

A: The objective of this question is to understand how to derive the scalar equation of a plane using…