3: One way to try to determine the line of intersection of two planes in 3-space is to find two points of intersection. Once you have two points, the line through them must be the line of intersection. To find two such points, it may help to search for points that are in both planes and have one of the coordinates x, y, or z equal to zero. (a) Explain the geometric idea behind this method. (Visualize and think..)

Q: 6. Find the intersection of the line / and the plane . 1:7=(4,-1,4) +t(5,-2,3) x: 2x+5y+z+2=0

A: Given is the equation of line as l:r→=(4,-1,4)+t(5,-2,3) Equation of plane as π: 2x+5y+z+2=0 First…

Q: -1 and Determine an equation of the line of intersection of the planes 2x – y + 3z x + 4y – z = 2

A: I

Q: 13. Find the distance between the two given parallel planes. x+y-3z = 4 x+y-3z=12

A: Given that:

Q: B. 3. A

A: Explanation of the solution is given below...

Q: Explain why it is impossible to find four points on the same plane equidistant from each other.

A: Let us imagine that we have 3 points in a plane that are equidistant from each other. These points…

Q: 9. Give a geometrical interpretation of the intersection of the planes with equations x+y-3=0…

A: Give a geometrical interpretation of the intersection of the planes with equation. x+y-3=0 y+z+5=0…

Q: give a geometric description of the set of points in space whose coordinates satisfy the given pair…

A: Given: x2+y2=4z=y

Q: give a geometric description of the set of points in space whose coordinates satisfy the given pair…

A: given,       x2+y2=4and z=0

Q: 29. In each case, determine whether or not the point lies on the line. If it does not, give an…

A: The line passes through the point B=3,-3,1 and has direction vector v→=4,4,1. Another vector in the…

Q: Quadrilateral EFGH has the vertices E(0, 0), F(a, 0), G(a + b, c), and H(2b, 2c). Verify that EFGH…

A: Given, EFGH is a quadrilateral which has vertices E(0,0), F(a,0), G(a+b,c) and H(2b,2c)

Q: True or false: A. A line is convex B. A half plane contains its edge C. A plane is the union of its…

A:

Q: Q4. Find an equation of the plane that passes through the origin and the point (1,1,1) and is…

A:

Q: At what point does the plane through A = (1,0, 0), B = (2,1, 1), and C = (-1,3, 4) cross the y axis?…

A:

Q: b) Determine, showing steps, whether the line [x, y, z] = []+¹] intersects the plane: 3 x + 7y + 8z…

A: We have to find the intersection of plane and line.

Q: Give a geometric description of the set of points (x, y, z) satisfying the pair of equations z = 0…

A: given: the set of points (x,y,z) satisfying the pair of equations z=0 and x2+y2=1. as we know that…

Q: 30 0= +시 +씨 2 |and 3x-y-z=3 -8/

A:

Q: 5. Consider two distinct points [b1 in the and plane. Explain why the solutions of the equation det…

A:

Q: 4. Which statement is never true for two planes? c) a) They intersect at a point b) The intersect at…

A: Which statment is never true for two planes

Q: 10. Paralleogram ABCD has vertices A(-1,4), B(3,2), c(3,-4), and D(-1,-2). y A(-1, 4) B(3, 2) 4-2 2…

A: Given, Parallelogram ABCD with vertices  A-1, 4B3, 2C3, -4D-1, -2  We have to find the equation…

Q: 3. Write an equation of the plane that is determined by the lines given by == and ==국 -2 z-2 -3 4 -1

A:

Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: Use equation of plane

Q: (a) Find the point at which the given lines intersect. r = (3, 2, 0) + t(2, –2, 2) r = (5, 0, 2) +…

A: Consider the equations of lines

Q: 1. Give a geometric description of the set of points in space whose coordinates satisfy the given…

A: Given: Let us consider the given set of points, a) x=-1, z=0 b) x2+y2+z2=25, y=-4 c) x2+y2=4, z=-2

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: Given that: y2+z2=1, x=0

Q: An equation in general form for the plane passing through the point (-5, 0, 2) that is perpendicular…

A:

Q: 5) The equation for the plane through A(2, 0,0), B(0,1,0), C(0,0,5) is

A:

Q: The third question: Let (1-, 1-, 1-) Q be a point in space and let us have the line L whose equation…

A: Let the equation of the plane passing through the point Q-1,-1,-1 be ax+1+by+1+cz+1=0…

Q: Find the equation of a) the line passing through the point (2, 1, 0) and parallel to the line X =…

A: Find the equation of (a) the line passing through the point 2,1,0 and parallel to the line x=5+2t ,…

Q: (a) Find an equation for the line of intersection between the planes z+3y-z = 2 and 2x –y+2z = 5.…

A:

Q: 14. Determine an equation of a plane parallel to a coordinate plane that contains the given pair of…

A:

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: Consider the set of points in space whose coordinates satisfy the given pairs of equations. x2 + y2…

Q: 29. BUILDING The roof and exterior walls of a house represent intersecting planes. Using the image,…

A: In the given figure, only four planes are shown. The intersecting lines formed from the intersection…

Q: QUESTION 2 Determine whether the three planes: X +2y + 32= 1, y +4z = - 1, and5x +6y = 2 have a…

A: Three planes are given. We need to check whether they intersect. If so, then we need to find the…

Q: 1. Find an equation of the plane through the points A(0,4, 6), B(5, 1, –1) and C(2,6, 0).

A:

Q: A quadrilateral has the vertices D (-4, -1), E (0, -4), F (6.0) and G (0.4). Verify for each pair of…

A:

Q: 2. Find the coordinates of the y-intercept of the plane (x, y, z)=(4,6,5) +s(2,3,1) + t(3,6,12)

A: To find out the coordinate of y-intercept.

Q: 3. What is the distance from the line to the plane? 7-(2,3,8)+(1.1.1) 2x - 5y + 32 + 10

A:

Q: 7) The equation of a line in the plane is ax + by + c = 0. Given two points on the plane, show how…

A:

Q: Determine an equation for each of the lines described below: • Line of intersection of the planes 2x…

A:

Q: 10+ 10-8-6 -2 10 4. -4 9- 10 What is the distance between point A and point B on the coordinate…

A:

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: y=0, z=0

Q: 2- Find un equation 6f the Plane containing the Points (0,0, 2 ), o (2,q!) (-2,3,3).

A:

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: x2+y2=4, z=0

Q: The diagram shows AB graphed on a coordinate plane. B (4, 6) 6- -5 4 3 2 -5 -4 -3 -2 -1 4 -1- -2 3…

A:

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: Given that, x2+z2=4y=0

Q: Your task in this section is to illustrate the situation below and make your own design of different…

A:

Q: Graph the plane: II = {(a + B,a + Y, B + y)[ a, ß, y ER, a + ß + y = 1}

A: To graph the below plane. α+β,α+γ,β+γ|α,β,γ∈ℝ,α+β+γ=1

Q: 29. In each case, determine whether or not the point lies on the line. If it does not, give an…

A: Since we have given a point and a line -

Q: Which of the following are symmetric equations for the line of intersection of the planes 2x+y+−6z=2…

A:

Q: In a geometry class, students are asked to describe the dimensions of a plane based on the…

A: The statements given by students are Mark states that a plane has zero dimensions because it is made…