20. The Cartesian equation of the plane which contains the point (1, -2, 3) and perpendicular to x-7 the line y-3 Z+10 is 2 1 2 A. x + 2y+ 2z = 11 B. x - 2y + 2z = 3 C. x+2y+2z = 1 D. x + 2y + 2z = 3

Q: 5. Determine the equation of the plane that contains the point (0,3,0) and the X = 1 line y = 2t z =…

A:

Q: 2.) Find the Symmetric form of the equation of the line of in tersection of the two Planes X-Y +Z…

A: Let a, b and c be the direction ratios of the required line. Since the required line lies in both…

Q: If Ax+By+5z=C is an equation for the plane containing the point (0,0,1) and the line x-1=2, z=-63,…

A:

Q: The equation of the plane that contains the three points (1, 2, 0), (1, 3, 1), and (3, 0, 4) is 6x…

A: Cartesian equation of a plane passing through three non collinear points A(x1,y1,z1), B(x2,y2,z2),…

Q: 2 2. Find an equation of the plane containing the point P(0, -) and the line determined by the two…

A:

Q: (1) Find an equation for the plane that passes through the point (–1,2,2) and contains the line of…

A: Given: Equation of planes x+y-z=5⇒x+y-z-5=0 and 3x-y+5z=3⇒3x-y+5z-3=0 and point -1,2,2, To find: The…

Q: 8. Determine the Cartesian equation of the plane that contains the line 7=(2, 3. 2) + 1, 1.4), te R.…

A: According to guidelines we solve one question.thanku

Q: 1. The plane containing the point (1,-5,8) and orthogonal to the line given b x=-3+15t, y=14-t,…

A:

Q: A linear combination of of u = 3 and v= 4 will give a plane in R³. Given that the point (2, 1, −1)…

A: Consider the given linear combination, u=132 and v=-144 will give a plane in ℝ3. The equation of a…

Q: 1. Find an equation of the plane that contains the line r = -2+ 3t, y = 4+2t, z = 3 - t and is…

A: We have to find

Q: An equation of a plane P passes through the point (0,0,-3) and perpendicular to the line L:x = 1-2t,…

A:

Q: The Cartesian equations of the line perpendicular to the plane 2x -3y + 4z + 8=0 and passing:…

A:

Q: Find an equation of the plane that passes through the point (1,-1,1) and contains the line of…

A: Let P=(1,-1,1) and n1=<1,1,-1> ,n2=<2,-1,3> The vector a for the line of intersection,…

Q: Find an equation of the plane that contains the line l(t) =(-1,1,2)+t(3,2,4)y which is perpendicular…

A: As given by the question There are given that the equation of line: lt=-1, 1, 2+t3, 2, 4 And, The…

Q: Find the intersection of the plane 4x – 6y – 7z = 10 and the line r(t) = (- 8, – 3, 3)t + (4, 1, 5).…

A:

Q: 6. Find an equation of the plane through point P(2, -4, 2) that contains the line F(t) = (2+ 3t, t,…

A:

Q: 4) Find the equation of the plane that passes through the point (6,0, 2) and contains the line x = 4…

A: The plane that passes through the point (6, 0, 2) and contains the line x = 4 − 2t, y = 3 + 5t, z =…

Q: Find an equation for the plane through P(1,4, 4) that contains the line of intersection of the…

A:

Q: 15. Find an equation of the plane through the point (-2, 4, 6) and perpendicular to the line r = t,…

A:

Q: Find an equation of the plane through (0, –9, –1) that is perpendicular to the line x – 2 = 3t, y +…

A:

Q: Find the intersection of the line r(t) = (2, 1, 3) + t(3, -3, 1) and the plane 4x - 4y - 2z = 6.

A: Given, Line-> r(t) = (2, 1, 3) + t(3, -3, 1) Plane-> 4x - 4y - 2z = 6 ------equation 1

Q: Find the equation of the plane that passes through the point (−1, 2, 1) and contains the line formed…

A:

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. Find the equation of the plane through P(1,1,4) that is parallel to the plane x+ 5y – z + 8 = 0

A: The scalar equation of parallel planes differ only by a constant Therefore, equation of the required…

Q: The plane equation that has 2.5 units distance to the plane 5x- 2y + 3z = 4 is %3D O a.…

A: Option (d) is correct.

Q: The equation of the plane through P.(2, 4, :5) perpendicular to the line :X = 5 +t ,Y= 1+ 3t , Z= 4t…

A: (.)  Let the point Px1,y1,z1 and perpendicular line  x-x0a=y-y0b=z-z0c Then the equation of the…

Q: 4. Find an equation for the plane in R³ spanned by the points (1,5, 1) and (1, 4, 2).

A: The two vectors are given as v1 = 151v2 = 142 Let xyz∈span{v1 , v2} Then xyz = mv1+nv2= m151+n142=…

Q: Find the equation of the plane that contains both of the lines given below. Line 1: x = 1+t, y = 2+…

A: Line 1 : x=1+t, y=2+2t, z=3-t        ⇒a⇀=1, 2, 3, l⇀=1, 2, -1 Line 2 : x=1-s, y=2+4s, z=3+2s…

Q: Find the general equation of the plane perpendicular to the line z – 2 y + 4 1- x = 3 and is 3…

A: We have to find the equation of plane.

Q: Find the equation of the plane that contains the line 2 5-x 2+y – 5 – z, and the 3 point P( 0,5,2).…

A: We have to find the equation of the plane that contains the line and the point.

Q: 2. Find an equation of the plane determined by the points P(1,1,0), Q(1,0,1) and R(0, 1, 1).

A:

Q: Determine the point at which the line passing through the points P(1, 0, 6) and Q(7, -1, 7)…

A:

Q: What is the equation of the plane containing point (3,0,4) and orthogonal to the line…

A:

Q: 19. (1) Give the equation of the line going through (3,2, 7) and orthogonal to r+ 2y - 3z = 16 (2) *…

A: 19) 1 Equation of ine through x0,y0,z0 having direction ratios a,b,c is x-x0a=y-y0b=z-z0c

Q: Find the point in which the line through P(3, 2, 1) normal to the plane 2x - y + 2z =-2 meets the…

A: Direction ratios of normal to plane 2x - y + 2z =-2  are <2,-1,2>, since line is normal to…

Q: Give the general equation of the plane containing the point (3,-1,4) and x 2-2 perpendicular to the…

A: The given equation of the linex2=y=2-z-3which can be written asx-02=y-01=z-23.The given point is…

Q: 6) = Find the point at which the line intersects the given plane. x =3 - t, y = 2 + t, z = 5t; x - y…

A: Equation of a Line in Parametric Form: where are functions of and is the parameter The equation of…

Q: 4.)It is known that the plane α passes through the point (2, 1, 3) and contains the line g with the…

A:

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

A:

Q: Find the equation of the plane that passes through the point (1,0,-2) and contains the line with…

A:

Q: The intersection point of the line whose equation is (x+2y+z=1),(x+y+2z=-1) with the xz plane is:

A: we have given x+2y+z=1  ...(i)x+y+2z=-1  ...(ii)solve it  2×(i)-(ii)x+3y=3   ...(a) this is equation…

Q: 2) Find the symmetric equation of the line containing the point (1, 2, 1) and perpendicular to the…

A: consider the direction ratio of line  contaning the point ( 1, 2 ,1 )  is  l , m, n

Q: what is the equation of the plane perpendicular to the intersection line of the x-2y+2z= 3  and…

A:

Q: 1. Determine the point of intersection of the line and the plane if it exists. π: 7x+y+ 5z = 0 x-4…

A:

Q: 4. What is the equation of the plane through (-1,-1,0) parallel to the plane x + 2y + 3z = 9? (a) x…

A: To find the equation of the plane through (-1,-1,0) parallel to the plane x+2y+3z=9

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: 9. Determine the Cartesian equation of the plane that contains the intersecting lines: -2 y 2+3 x-2…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.