8. Let P(1,2,3), Q(1,-1,-2), and R(0,0,0) be the three points in R³ a. Find an equation of the plane through P, Q, and R. The coefficient on x should be -1. b. Find the area of the triangle formed by PQR c. Find the equation of the line through P that is perpendicular to the plane from (a) - hint: use the line when the x = -t+1 if the line is in the form

Q: nd the distance from the point to the plane.   (3,3,8)​, 7y+3

A: Given, the equation of plane is                                       7y+3z=0and  point (3, 3, 8)

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: .Find the equation and sketch the plane that contains the points (2, 6, 1), (-4, 9, -1) and (4, 3,…

A: Equation of plane is 3x+2y+6z = 12

Q: Let P = (1, -2,3); Q = (3,-2, 4); R = (2,-1,5) & S = (5,0,-2). Answer each of the following: (1)…

A: Points: P = 1,-2,3 ; Q = 3,-2,4 ; R = 2,-1,5 ; S=  5,0,-2 Aim: To find the area of triangle PQR.…

Q: 9. Find the equation for the plane through Po(-2,3,9) perpendicular to the line x = -2 – t, y = -3 +…

A:

Q: etermine the intersection point of the two lines or show that they do not intersect. a. Does the…

A: Given: (-5,4,-1) and (-3,-5,0)

Q: O(0,0) and A(4,4) are two given points and B is any point. Find the equation to the locus of the…

A: Given The O(0,0)  and  A(4,4) are any two points and  B is any points . OB and AB are perpendicular…

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: Plot the following sets of points in a Cartesian plan given set of points consecutively to form a…

A:

Q: Find the vertices of the triangle whose sides are the lines x = 0, x + y + z = 0, and 3x - 4y + 5z =…

A: Sol:- we need to find the points where these lines intersect.We'll denote the first intersection…

Q: . Let A=(2, 3, 1) and B= (4, -1, 2) and C = (6, 2, 3). Find the equation of the line in parametric…

A:

Q: C. Find the equation of the plane passing thru P;(-1,2, –3) and perpendicular to the line through…

A:

Q: Let A be the point with coordinates (-2, -1, -1) and let B be the point with coordinates (2, 0, 0).…

A:

Q: Find the point of intersection of the line with equation (1,8,3) + t(1,-1,3) and this plane. What is…

A: Now we will find the point of intersection.  And we  will find the y coordinate of this point

Q: Let A:(-1, 1, –1), B:(2,0, 2), C:(4, 1, –3), and D:(-3, 1, 10) be points in R. (a) Find the angles…

A: Since you have posted a question with multiple sub-parts, we will solve only first three sub-parts…

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

A:

Q: ) Find an equation of a line that is perpendicular to both u = and v m and contains the point (2,3,…

A:

Q: 3) Find equations for the lines: h the no e. The line through (1,1,1) parallel to the z-axis. f. The…

A: