[V] Find the three intercepts of the plane 3x +y + 2z = 12 and use them to sketch the plane. How would you work out the area of the triangle in the plane that is formed by these three intercepts? (Don't do the calculation: Just explain.)

[V] Find the three intercepts of the plane 3x +y + 2z = 12 and use them to sketch the plane. How would you work out the area of the triangle in the plane that is formed by these three intercepts? (Don't do the calculation: Just explain.)

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 35E

See similar textbooks

Related questions

Q: Find an equation for the plane that passes through the point (-7, 10, –8), is parallel to the line x…

Q: Find the point, P, at which the line intersects the plane. x= - 3+ 10t, y = 9- 9t, z= 9- 7t; - 10x +…

A: The objective is to find the point of P, at which the line intersects the plane.

Q: 32. Find the equation of a plane through the origin and per- pendicular to x – y+ z = 5 and 2x + y–…

A: Note- According to Bartleby guidelines, we are supposed to do only one question. If you want more to…

Q: 2:- find the line of interSection o f the plane -2x + 73 - 2324 given by 3x t6y-52=-3 f the plane

Q: what is the equation of the plane parallel to the xy-plane and passing through the point P0=(1 0…

A: We can write the equation of plane in general form and satisfies by given point

Q: Find any line equation that does not intersect the plane 2x – 5y + 3z 4. -

Q: Find the equation of the plane through the line of intersection of the planes x+y+z=1and 2x+3y+4z=…

A: The equation of the plane through the intersection of the planes, x+y+z=1 and 2x+3y=4z=5, is…

Q: Find the equation for the plane through Po(7.- 3. - 1) perpendicular to the following line. x=7+t,…

A: Ans equation of line x=7+t, y=-3-3t, z=-2t or x-71=y+3-3=z+0-2

Q: 2) The distance between the parallel planes ax + by + cz + d1 = 0 and |d1-d2| ax+by+cz + d2 = 0 is…

A: We find required equations of plane parallel to given plane.

Q: Find the equation for the plane through Po(- 4,8, - 3) perpendicular to the following line. x = - 4…

Q: Find an equation of the plane. The plane that passes through the line of intersection of the planes…

Q: What is the equation of the plane through (-1,-1,-1) parallel to the plane x+ 2y + 3z = 9?

A: The vector normal to the plane ax+by+cz=d is ai^+bj^+ck^ . The plane parallel to this plane has the…

Q: Find the equation of the plane through the point P = (2, 5, 4) and parallel to the plane 5x – 5y +…

A: Equation of plane parallel to 5x -5y +3z = 6 is given by; 5x -5y +3z + λ = 6 Also it passes…

Q: Find the equation of the plane through the line of intersection of the planes x+y+z=1 and…

Q: Find the point in which the line X = 2, y = 3 + 2t, z = -2 – 2t; meets the plane 6х + Зу - 4z 3 -12…

A: The point of intersection will satisfy the line as well as the Planes equation.

Q: Find an equation of the plane. The plane that passes through the line of intersection of the planes…

Q: Find an equation for the plane parallel to – 2x + 9y – 2z 30 and containing the point (1, 4, 3)

Q: Find an equation of the plane that is parallel to the plane x + 7y – 2z + 20 = 0 and contains the…

Q: Find the point in which the line X = 2, y = 3 + 2t, z = -2 – 2t; meets the plane 6х + Зу - 4z -12…

A: the point at which the line meets the plane is (x,y,z) = (2,-207,277)explanation is given in below…

Q: Determine the equation of the plane that passes through (2,-4,1) and is perpendicular to the line of…

A: A plane is passing through 2, -4,1 and perpendicular to the line of intersection of the plane 3x -…

Q: Find an equation of the plane that crosses the x-axis at 3, the y-axis at 2, and the z-axis at 5.

Q: 286. Find the general equation of the plane that passes through the origin and is perpendicular to…

Q: Find the intersection of the line and the plane. 2x + y = 3, r(t) =〈2, -1, -1〉+ t〈1, 2, -4〉

A: We have to find the intersection of the plane 2x+y=3 and the straight line r(t)=2,-1,-1+t1,2,-4

Q: The equation of the plane which is parallel to y -axis and cuts off intercepts of length 2 and 3…

Q: What is the real number a that makes the line 2 -1 y-12 z-7 a -2 3 parallel to the plane z -y - 2z=…

Q: Determine the scaler equation of the plane with × -intercept=2, y intercept=-1 and z intercept=3

Q: 25. Find an equation of the plane through the line of intersection of the planes x – z = 1 and y +…

A: Equation of a plane P that passes through the line of intersection of two planes P1 and P2 is given…

Q: 1. Determine the point of intersection between the line, L: x = 3+t, y=4-5t, z=1-7t, te R, and the…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 9-The distance d between the parallel planes -2x+y+z 0, 6x-3y-3z-5-0 is: a) V54 b) 54 V5 d) 3 c) e).…

A: Distance between two parallel lines

Q: Find the point closest to the origin on the line of intersection of the planes y + 2z = 12 and x + y…

Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 7z + 13 =…

Q: Consider the lines x – 4 l2 : 4 - 1 l1: x= 4 – 3t, y = 2t, z = 1 + 5t , %3D 2 (b) Find an equation…

A: Given that: Two lines are: l1: x=4-3t, y=2t, z=1+5t, l2:x-44=y1=z-12

Q: Find the distance between the parallel planes – 2x + y + z = 0 and - 10x – 5y – 5z – 11 = 0. - NOTE:…

Q: Find the distance between the parallel planes P1: 2x – y + 2z +6=0 and P2:6x- 3y+6z- 18 = 0

Q: Find an equation of the plane through the origin that is parallel to the plane 4x-3y+5z+13=0

Q: Find the distance between the parallel planes P1: 2x – y+2z + 6 = 0 and P2: 6x - 3y+ 6z – 18 = 0 3y…

Q: Find the equation for the plane through Po(-7,- 4,7) perpendicular to the following line. x= -7+t,…

A: Solution: The objective is to find the equation for the plane through the given point and…

Q: For the plane, 6x + 10y + 15z = 30, the values of the x-, y-, and z-intercepts are %3D 5, 3 and 2 3,…

Q: Find Angle between -3/2x-6y+z=4 and 2x-y-1/2z=7 find an equation for the line L of intersection of…

A: The objective is to find angle between two planes and equation of line passing through the…

Q: Determine the general equation of the plane 2 passing through the point P(1,-4,-5) and parallel to…

Q: Find an equation of the plane that is parallel to the plane x+ 2y – 10z + 12 = 0 and contains the…

A: The equation of the given plane is x+2y-10z+12=0 We need to find the equation of plane that is…

Q: Find the equation of the plane through Po (2,-1,-1) and P1(1,2,3) and perpendicular to the plane…

Q: C:- find the line of interseetion of the plane -2x +7-2=24 given by 3x +6y-52=-3 f the plane

Q: Find the point of intersection of the lines L1 and L2 and determine the equation of the plane that…

A: Point of intersection of two lines in 3D

Q: Find the equation of the plane through the origin that is parallel to the plane 4.r – 2y+ 7z +12 = 0…

A: Consider the general equation of a plane, 4x-2y+7z+12=0 the normal vector of this plane will be…

Q: Find the equation of the plane through Po (2,-1,-1) and P1(1,2,3) and perpendicular to the plane…

A: Given: P0(2,-1,-1) and P1(1,2,3) 2x+3y-5z-6=0

Q: Q1. Find the equation of the plane determined by the lines : L₁: (x = -2+1, y = 21 +3₁ Z=4-1), L₂:…

Q: Find the equation for the plane through Po(4,- 5,5) perpendicular to the following line. x= 4 + t, y…

A: ee

Q: Find the point, P, at which the line intersects the plane. x=-5-6t , y=9-8t , z=8+7t ; 2x-4y-9z=-2…

Q: Which of the following planes is the equation for the plane with an x-intercept at P(2,0,0), a…

Question

3. [V] Find the three intercepts of the plane 3x +y + 2z = 12 and use them to sketch the plane. How would you work out the area of the triangle in the plane that is formed by these three intercepts? (Don't do the calculation: Just explain.)

Expert Solution