5. A plane n passes through the following points: A (1,0, -7); B (-2, -1.0); C (0.0, -3). a-) Find the point of intersection of this plane with the line D of equation x-7_ y+1 z-2 12 -6 -2 (Suggestion. - Solve the system composed of the normal (or linear) equation of the (x-7 y+1 12 -6 plane and the following two equations: x-7 z-2 %3D 12 -2 N.B. - These equations define the line.) II

Q: Find the equation of the plane through (-1,4,2) and containing the line of intersection of the…

A:

Q: 1. Find an equation of the plane that passes through the points (-1, 3, -3), (4, 1, 2), and (8, 2,…

A:

Q: 5. Find the equation of the plane containing the points P(3, 2, 1), Q(2, 1, -1), and R(-1, 3, 2)

A: Let position vectors of point P(3,2,1) , Q(2,1,-1), and R(-1,3,2) are a→,b→ and c→

Q: in 4 method ТВС- тво-1 Example 1.8.6 Find the p sic equations of the plane that passes through the…

A:

Q: 6. Find equation of the plane passing through the points (2, 0, 3), (1, 2, 3), and (-3, -1, 5)

A:

Q: 6. Find the equation of the plane that passes through (3,1,2) and (-1,2,–1) and is parallel to the…

A:

Q: 8. Find the equation of the plane that contains the points P,(3,1,–2), P2(0, –2, 1), and P3(-2, –5,…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The line through the points (−3, 8,−4) and (1, 0, 8) intersects the yz-plane at _____.

A: We know that equation of line which passes through two pointsx1,y1,z1,x2,y2,z2 is given by…

Q: 16- Find the equation of the plane that contains the line = 2+ = 5-z, and the point P(0,5,2).

A:

Q: 20) Find the equation for the plane in 3-space passing through the points (2,3,2), (0, -4, 3) and…

A:

Q: 7. Find the equation of the plane passing through the points (1, 1, 2), (3, –1,6) and (5, 2,0).

A: To find the equation of the plane passing through the given points

Q: Find the equation of a plane passing through (2,1,3), (3, –1,5), and (1,2, –3).

A: Equation of plane

Q: (a) The curve with equation 2 y 3 + y2 - y 5   = x 4 -2x3  +x 2  has been likened to a bouncing…

A:

Q: 10. Find an equation of the plane that passes through the points (x, y, z) = (1, 2, −1), (x, y, z) =…

A:

Q: 7. Show that the equation of the plane that has x-intercept a, y-intercept b, and z-intercept c…

A:

Q: 4- Find an equation of the plane that passes through the given points (-2, 1, 1), (0, 2, 3), and (1,…

A:

Q: 2. Find the equation of the plane through the points (1, -3,2), (3,0,– 1), and (0,5,5).

A:

Q: Find an equation of the plane through the three points given: P = (0, 1, 0), Q = (-3, 4, – 1), R =…

A: Recall: Equation of the Plane containing three points P,Q and  R is expressed as ,            r→ .n∧…

Q: Find the eu. f line through the Pont (-2,3,4) and Parallel to e Planes: 2x +3y +42-5, 3X+4y+52 - 6…

A:

Q: 3. Find an equation of the plane passing through the points (-1,2,0), (2, 3, 6), and (-1, 5, 2).

A:

Q: Find an equation of the plane passing through P = (1, 2, 3), Q = (0, 0, 3), and R = (−2, 5, 4).

A:

Q: A plane through the three points P = (4, -3, 5), Q = (-2, -3, 5), and R= (-2, 3, -3) is described by…

A:

Q: as If the equation of plane passing through the mirror image of a point (2, 3, 1) with respect to…

A:

Q: 4. Find an equation for the plane in R spanned by the points (1, 5, 1) and (1,4, 2).

A: Given v1 = (1 , 5 , 1)v2 = (1 , 4 , 2) Let xyz be a point in spanv1 , v2 , so there exist m , n…

Q: 9. Find an equation for the plane containing the points (3,1, 4), (–1, –1,-1), and (0,2,2).

A:

Q: 2. Find the equation of the plane through the points (1,–3,2), (3,0,–1), and (0,5,5).

A: The solution is given as follows

Q: . Find an equation of a plane passing through the point (3, 4. 0) and containing the line of…

A:

Q: 5 Find the equation of the plane passing through the points A(1, 2, –3), В(2, 1, 4), С(3,0, 1).

A:

Q: Find the linear equation of the plane through the point (0, 1, 1), (1, 0, 1), and (1, 1, O)

A: Consider the point (0,1,1). Take option (a) x-y-z+2=0-1-1+2=0 Take option (b) -x+y-z+2=-0+1-1+2=2≠0…

Q: 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

A: Given problem:- 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

Q: 5. Find the equation of the plane that passes through the point (6,0,-2) and contains the line X =…

A:

Q: 16- Find the equation of the plane that contains the line = 5 - z, and the %3D point P( 0,5,2).

A:

Q: 4. Determine the equation of the plane passing through the point (1, –4, 3) and parallel to x – y…

A:

Q: Find equation of the plane through (1,0,-1).(-1,2, 1) and parallel to the line of intersection of…

A:

Q: Find the equation of the plane through the points (1, -1, O), (1, 0, 1) and (2, 2, 1).

A:

Q: Find an equation for the plane through points P(1, -1,2), Q(2,1,3) and R(-1,2,–1).

A: This question can be solved by applying the formula of equation of plane passing through three non…

Q: 8. Consider the parabola whose equation is y=x² -4x and the line whose equation is y=2x+b, where b…

A: y=x2-4x  &  y=2x+b Put y=2x+b in y=x2-4x, we get ⇒2x+b=x2-4x⇒x2-4x-2x-b=0⇒x2-6x-b=0 To intersect…

Q: Suppose a surface in three-dimensional space has the equation ax^2+bx+cy^2+dy=z  and it contains the…

A: A given set of points can be assumed to be on a surface given by an equation when the each of…

Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x-y + z =…

A:

Q: The equation of the plane that passes by P(-1, 2, 1) and that is perpendicular to the line x - 3 1-…

A:

Q: Find the points at which the line that passes through (–6,6,4) and (12,–6,2) intersects the three…

A:

Q: Find an equation of the plane through the three points given: P = (0,0, 2), Q = (-4, 1, –1), R = (2,…

A:

Q: Find a plane containing the point ( - 5, - 5, 2) and the line r(t) = (1, - 2, 1) + t(4, 7, 5).

A: First you will find the normal vector to the plane and then find the value of the constant d

Q: Find a plane containing the point (-7,-3,-2) and the line of intersection of the planes 3x – 2y – 3z…

A:

Q: Find an equation of the plane through the three points given: P=(0,0,3), Q=(2,−3,2), R=(−1,1,0)

A: find the equation of the plane

Q: Find the equation of the plane that passes through the point P = (1, -5, 2) that has normal n = (-4,…

A:

Q: The equation of the plane containing the points (4, – 3,1), (-3,–1,1) and (4, –2,8) is:

A: