Linear Algebra Let α be the plane that passes through the origin and is perpendicular to the line that joins the points A(1, 0, 0) and B(0, 1, 0). Find the distance from point C(0, 0, 1) to plane α

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

A:

Q: Lines in the xy-plane Show that A(x - x0) + B( y - y0) = 0 is an equation for the line in the…

A: The line of an equation will be determined if one point is known from which line is passing and…

Q: Find a parametrization of the line in which the planes x- 2y - 2z = 3 and -3x + 3y + 3z = -6…

A:

Q: (a) Find the point at which the given lines intersect. r= (1,3, 0) + t(3, -3, 3) r = (4, 0, 3) +…

A:

Q: 2. Find a plane perpendicular to the planes x + y - 3z = 0 and x - 2y-2z = -1. Your answer

A:

Q: Find the linear equation of the plane through the point (2,3,6) and parallel to the plane…

A:

Q: ind an equation of the plane that passes through the points P, Q, and R. P(2, −1, 3),  Q(3, −2,…

A: We have to equation of plane

Q: (A) Find the angles between the planes 2 x + 2 y+ 2z = 3 and 2x- 2 y-z = 5 (8) Find the distance…

A:

Q: A point in space and let's have the line L whose equation is Q(-1,0,1) let 1 L: 3- x = y = 4 4 It…

A:

Q: Coordinates of point which partitions a directed line segment AB at the ratio of a:b from A(x1,yı)…

A: Section formula we need to use

Q: passing through the origin and point A (1,1,1) What is the equation for the plane perpendicular to…

A:

Q: Parametric equations for the line containing (3,-1,4) and (-1,5,1) are: O x = 1- t, y = 3 + 6t, z =…

A:

Q: Find the plane containing the intersecting lines: L1: x = -1 + t, y = 2 + t, z = 1 - t; -∞< t < ∞…

A:

Q: How do you solve for square roots in fractions? Im suppose to solve the midpoint of the line joining…

A: Given formula is M = (x1 + x2)/2

Q: (a) Find the point at which the given lines intersect. (1, 2, 0) + t(2, -2, 2) = (3, 0, 2) + s(-2,…

A:

Q: The vertices of AJKL are J(-3, 4), K(3, 0), and L(-5, -4). The equation of the median JLis y = 0.…

A:

Q: Find a parametrization of the line in which the planes x-2y -2z = 3 and -3x + 3y + 3z = -6…

A: We have to find value of x, y and z

Q: Let r be the straight line that passes through the point A(3,6,4), intersects the z axis and is…

A:

Q: Q2/ Let Li be the line through the points (1, 2, 6) and (2, 4, 8). Let L2 be the line of…

A:

Q: Linear Algebra Let "r" be the line determined by the intersection of the planes x+yz= 0 and…

A:

Q: nterseeting Lines Finad the plane determined by the Loi Xi=l-2t, , J="l-st,, 2= -2+t, L2: X2=-3+t2,…

A:

Q: ind the egu. f Plane Passes through the Paints A(I,1-1) B(2,0 2) and C (0,-2,1) ? 7x-5५-१Z-6 ans.

A:

Q: The equation of a plane is (X,Y,Z)= (1,0,0) + s(-1,0,-1) + t(-1,2,0),s,t ER. Determine the vector…

A:

Q: 3. PQ lies in the standard (x, y) coordinate plane. What are the coordinates of the midpint of PQ if…

A:

Q: Repeat Exercise with b1 b2 , and A = Exercise Let S be the parallelogram determined by the vectors…

A:

Q: Show that planes 2x- y + z = 0 and x+2y-z = 1 intersect according to a straight r.

A: General Equation of a Plane: A plane can be represented by an equation of first degree in such as…

Q: Algebra Linear Find the equation of the line that passes through point A(1, 0, 1) and is parallel…

A:

Q: Give an equation of a plane described below. Determined by intersecting lines L1 and L2 L1: x = 2t y…

A:

Q: 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.

A: In this question we will use basic of calculus i.e equation of plane.  In question number 22.we will…

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

A:

Q: (v) Find the equation of the plane II that consists of all linear combinations of u, v. (vi) Is the…

A: use linear combination

Q: Linear Algebra  Determine the line r that passes through points A(4, 0, 1) and B(5, 1, 3). Then…

A: we have to determine the equation of a line r passing through points A(4,0,1) and B(5,1,3). then we…

Q: (0,4) (8,12.5) (6,7.5) Using the three coordinates from above, create a parabolic model H(x) in…

A: To find the equation of parabola

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;…

A:

Q: (a) Find the point at which the given lines intersect. r = (1, 3, 0) + t(3, -3, 2) r = (4, 0, 2) +…

A: Introduction: When a line in three dimensional Euclidean geometry passes through a point with a…

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: Find a non zero unit vecor û that is orthogonal to u1=(1,2,1) U2= (2,5,4) in R³.

A: Given; u1 = (1,2,1) and u2 = (2,5,4)

Q: through the points O(0, 0, 0), A(1, −2, 3), and B(2, 0, −2); (ii) through the point A(1, −2, 3) and…

A:

Q: 1. Find a non zero unit vecor ô that is orthogonal to u1= (1,2,1) and uz= (2,5,4) in R³.

A:

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

A:

Q: The plane perpendicular to the x-axis at (–2,0, 0) : The plane perpendicular to the y-axis at (0,…

A: the equation is  (x1,y1,z1)=passing points a(x-x1)+b(y-y1)+c(z-z1)

Q: r(u)=(a1u2+b1u+c1,a2u2+b2u+c2,a3u2+b3u+c3), u∈R lies in a plane, and find an equation of the plane.

A: Given:r(u)=a1u2+b1u+c1, a2u2+b2u+c2, a3u2+b3u+c3To find:The equation of the plane.

Q: 1) Let A = (0, 0, 0) and B = (2, 0, 0). a) Find a point C in the xy-plane that is a distance 2 from…

A: a) C is a point on the xy-plane with a distance of 2 from both A and B.Consider C = (x, y,…

Q: Find the cross product a x b. a = (t, 8, 1/t), b = (t2, t², 1) Verify that it is orthogonal to both…

A:

Q: Calculate the distance from point P(1, 0, 2) to the x + y - z = 0 plane.

A:

Q: Ноше work Find an equation of plane through the points pl (-1, 1, 1) and point intersection of the…

A: Here we have to find the equation of the plane passing through the point P1(-1,1,1) and point of…

Q: Determine the Cartesian equation of the plane that has x-, y-, and z-intercepts at 2, -4, and 3…

A: Since you have posted multiple questions we solved first question for you  To get the solution of…

Q: Exercise 9. Let u = (1,2) and v = (2, 1). Find a nonzero linear combination i of u and v that's…

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.