4. (a) (b) (c) For this problem, consider the planes P₁: x+y=z= 1, and P2: 2x + 3y + 5z = 5. Find the angle between P₁ and P₂. Find parametric equations for the line of intersection of P₁ and P₂. Find the point on P₁ that is closest to (2, 3, 1).

Q: Consider the points A=(2,7,-4) and B=(4,5,7) in R3, one way to write the parametric equation of the…

A: Given :- Consider the points A = (2, 7, - 4) and B = (4, 5, 7) in R³, To find:- one way to write the…

Q: Find an equation of a plane making an angle of π/2 with the plane 3x + y − 4z = 2

A: Here we have to find the equation of plane  making an angle of π/2 with the plane 3x + y − 4z = 2

Q: The parametric equations for a line L₁ are as follows: x=-4+6t y=3-4t z = 1+4t Let L₂ be the line…

A: The given problem is to find the point P on the line L2. Given Line L2 is parallel to line L1 and…

Q: Q1. The parametric equations of the lines L1, and L2 are given as: L: x=-2+1, y=3+2t, z=-t+4 L₂:…

A: Let's find distance between two lines.

Q: Find the equation of the circle which cuts the three circles…

A:

Q: genuy. Registration number = 026 II: Consider rx + y+ 4z = 8 and x + ry – z = -1 %3D Find the acute…

A:

Q: The lines L1 and L2 are determined by the following symmetric and parametric equations,…

A:

Q: 1: Find the angle between the planes 3x - 6y + 4z 3 and 2x - 2y +z = 4 then find the parametric…

A:

Q: Given the symmetric formula:   (x + 8)/2 = (y − 6)/3 = z − 7   Find the parametric formula of the…

A: The parametric formula can be obtained by equating the equation of given line with t

Q: For the plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. xVi.…

A: Given, x=t; y=2t-9; t x y 0 0 -9 1 1 -7 2 1.414 -5 3 1.732 -3 4 2 -1

Q: 1. Find the angle between the lines L,:x = 3 + 8t, y = -6t,z = –7+ 24t and L2:x = 3 + 8t, y = 15t, z…

A: Solving only ques 1 according to guidelines.

Q: Find the angle between the two planes x- 2y + z = 29, 2x + 3y – 2z = 6. And also find the parametric…

A: here we will find angle between two planes and parametric equation of plane's line of intersection,

Q: B) (10 M) Find the parametric equation of the line through the point p (-2, 0, 5)- and parallel to…

A: Let's find.

Q: 3.) the a. Find the distance between point and the line given by the set of parametric equations. (…

A:

Q: Q1: Two lines in space {x 1- 2t,y 2 +3t,z =-1+t} and {x = 1+t,y% 3+ 2t,z = -1+3t} find the angle…

A:

Q: 2. Give the parametric system of equations of the line given by the equations: 2x = 4 – 3y = ±1 Give…

A: