C. Find the equation of the plane passing thru P;(-1,2, –3) and perpendicular to the line through the points Q(7, –5, 2) and R(-3,9,4).

Q: (d) Find the Cartesian equation of the plane that contains both the line L2 and the point A

A: Introduction: The scalar product of two vectors OA and OB is given by, OA·OB=OAOBcosθ The vector…

Q: Find the equation of the plane through (1,-4,2) and per pendicular to each of the planes 2x t 5y -2…

A:

Q: Find an equation of the plane containing the point (3,0,-4) and perpendicular to the line r(t)=…

A: A detailed solution is given below

Q: Which of the following is the equation of the plane where x-2y + 32 = 3 and x+y+z=2 and passes from…

A:

Q: Show that the lines determined byr 1(t) = < 7, 3 − 4t, 2 + 6t> andr 2(t) = <6 − t, 3 + 8t,…

A: Given: r1(t)=7,3-4t,2+6t r2(t)=6-t,3+8t,9-5t For r1. x-7=y-3-4=z-26=t For r2. x-6-1=y-38=z-9-5=t…

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

A: Suppose a plane passing through the points x1,y1,z1 and a vector perpendicular to the plane is…

Q: Find a plane containing the point (6, -4,-3) and the line (t) = +t 270

A:

Q: Find the equation of the plane through P(4, 3, 6) and perpendicular to the line joining P(4, 3, 6)…

A:

Q: Find an equation of the plane containing the lines L1 and L2 in R3 L1: x = t ; y = -t ; z = t L2:…

A: We have to find equation of plane containg Line L1 and L2  -

Q: Find the equation of the plane containing the point P(1, 1, –1) and the line -4+t 1- t 1+t

A:

Q: Write the equation of the plane that contains the point P(1, 3, 5) and the line L: x = 4t, y = 6 +…

A: It can be solved using properties of plane.

Q: Q3/ Find the equation of the plane that contains the line 3-x 2+y %3D 3 - z, and the point P (1, 4,…

A: Given line is  3-x4=2+y2=3-zand the point is (1,4,3) find the equation of the plane

Q: Determine the equation of the plane that contains the lines Li and L2. L: x = 3- t, L2: x = 8 +2 s,…

A:

Q: Find the equation of the line given by the intersection of the following two planes: T1:-2x + 4y- z+…

A:

Q: Find an equation for the plane through P0(-3, 0, 7) perpendicular to n = 5i + 2j - k.

A: given that the plane passes through (-3,0,7) perpendicular to n=5i+2j-k. we need to find the…

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.

A:

Q: The line L(t) = (3+t, 12+5t, -12-5t) intersects the plane 5x - 5y = 15 at what point?

A:

Q: 1. Find the equation of the plane that contains the line point (1,3, 2). 무 =D북3부 md the

A: Let's find.

Q: which of the following is the equation of the plane that is passing through the point P(2,2,-2) and…

A: Given P( 2, 2, -2) and planes  x+2y-3z=3 and x+y+z=2

Q: draw the plane given by the equation  x + 2y = 6

A: To draw the plane given by the equation  x + 2y = 6

Q: Given the point P (2, 4, -1) and the line L: x 1+ 2t; y =2-5t; z 2 +3t Find the equation of the…

A:

Q: (50p.) l- Find an equation of the plane through (1,3,–2) and the line of intersection of the two…

A: Given that, P1 : x-y+z=1 P2 : x+y-z=1 and Point A(1,3,-2)   We have to find Equation of Plane…

Q: Find the equation of a plane through the intersection point of the lines r(t) = and 7(s)= where r, s…

A: The equation of plane is mainly given by the normal vector calculation. The normal vector to the…

Q: Find the equation of the plane containing the points P= (2, 0, 0). Q = (0, 2, 1), and R = (1,0, 3).

A: This question is based on finding equation of plane when we know 3 points of plane.

Q: Find the equation for the plane through Po(4,9,-7) perpendicular to the following line. x-4+t,…

A:

Q: O Find an equation for the plane through the point P = (3, −2, 4) that is perpendicular to the line…

A: Given problem:- Find an equation for the plane through the point P = (3, -2, 4) that is…

Q: Find the equation of the plane that contains the following two lines: I = -1+t, L1 : y = -t, I = -1,…

A: To find the equation of plane containing both the lines

Q: Q3/ Find the equation of the plane that contains the line 3-х 2+y = 3 – z, and the point P (1, 4,…

A: Equation of the plane

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2, –2)…

A: The equation of the plane passing through the points (x0 , y0 , z0) and perpendicular to a vector…

Q: H.W 7- Determine whether the four points P:(1, 1, 2), P:(4, 0, 3), P:(1, 5, 10), and P:(7, 2, 4) lie…

A:

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,–2) and…

A:

Q: Find an equation of the plane each of whose points is equidistant to the point H(4, 2, 5) and to the…

A: Basic 3D Geometry problem

Q: Find the equation of the plane that contains the line r¡(t) = (1 + lt, –1+t, 2+ 8t) and the point…

A:

Q: Given the point P (2, 4, –1) and the line L: x = 1+ t; y=2+ 4t ; = =-3t Find the equation of the…

A:

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

A:

Q: Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 15 –t and L2 : {…

A:

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,–2) and…

A:

Q: Write the equation for the plane through the point P(- 4,4,2) and perpendicular to the line x =4+7t,…

A: Explanation of the answer is as follows

Q: Find the symmetric equation of the line that is an intersection of the planes a: x-4y + 2z-2 = 0 and…

A:

Q: Write the equation for the plane through the points P(-1,6, - 61), Q(2, - 8,66), and R(1,- 7,53). O…

A:

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,-2) and…

A: To find the equation of the plane passing through the point P 2,2-2 and vertical to the line of…

Q: Find the equation for the line passing through and perpendicular to Hhe plane P= (!,2,-3)…

A:

Q: Find the equation of the plane containing the following two lines: L1 : te R 1 L2 : +s. seR 1

A:

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 (if it exists) at which the following plane and line intersect. y = - 10; r(t) = (4t…

A:

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

A:

Q: Let P = (2,0, –2) and l be the line given by -5 | 3 +t -3 15 3 The equation of the plane passing…

A:

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A:

Q: Find the equations of the line through (2,0, –4) and parallel to each of the planes x + y – z = 0…

A: