2) Find the equation of the plane that is orthogonal to the planes 3x-2y-2z=1 and x-3y-10z = 4 and contains the line r(t) =

Q: 11) Find the equation of the plane that passes through the point (1, 5, 1) and is perpendicular to…

A: A plane is passing through a point (1,5,1) and is perpendicular to the planes 2x + y - 2z = 2 and x+…

Q: 1. Find the equation of the plane that contains the point (-1, 1, 2) and the line given by x=1-t,…

A: This question is based on 3d geometry.

Q: Find an equation of a plane containing the line r = (2, –2, 3) + t(12, –8, 4) which is parallel to…

A: Equation of plane parallel to the plane 4x+4y-4z=-17 is of the form  4x+4y-4z=k This plane contains…

Q: Find the equation of the plane containing the line of intersection of the two planes z+y+z+5=0 and…

A:

Q: 20. Find the point at which the line a = 1+ 2t, y = 4t, z = 2 –t intersects the plane r+y – 2z +1=…

A: Given that, equation of line:- x=2t, y=4t, z=2-t Equation of Plane:- x+y-2z+1=0

Q: Find an equation for the plane through the point (0, –4, 5) which is perpendicular to the line…

A:

Q: Find an equation of a plane containing the line r = (4, –5, –4) + t (–7, 8, –4) which is parallel to…

A:

Q: Find the equation of the plane passing through the point (-1, 4, 0) perpendicular to the line L₁: x=…

A:

Q: Calculate the equation of the line that passes through the point (0, 1, 2) that is parallel to the…

A: We need to find the equation of the line passing through a point, parallel to a plane and…

Q: Find the vector equation for the line of intersection of the planes 5x +y-3z= -3 and 5x + z = -1 r =…

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: Find an equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the point…

A: To find the equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the…

Q: The intersection point of the line that passes through the origin and is perpendicular to the plane…

A:

Q: Find an equation for the plane passing through the point P(-2, 1, 1) and parallel to the plane 3x +…

A: Solve for the equation

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: At what point does the line :LiX==€ 1=10+8€ 14. -2y t52 +16:0 10+3€ z=41+3€ intersect with the plane…

A: Question is based on 3d Geometry.

Q: Find the point at which the line x=1+t, y=3-2t, z=1-t intersects the plane 2x+3y+3z=0

A:

Q: Find the equation of the plane through the point (1,2,-1) and parallel to the plane 2x- 3y+4z+6-D0.…

A: To find: The equation of plane passing through the point 1,2,-1 and parallel to plane 2x-3y+4z+6=0.…

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: Determine the general equation of the plane 2 passing through the point P(1, –4, –5) and parallel to…

A:

Q: Find an equation of the plane containing the line = 3t, y=2-4t, z = 1+ t and parallel to z-axis.…

A:

Q: Find a vector parallel to the line of intersection of the planes 2x + y - 3z =13 and x + 3y + 5z =-8

A: Given, The equation of the planes  2x+y-3z=13 x+3y+5z=-8 We have to find a vector parallel to the…

Q: Find the equation of the plane that contains point P1(1,0,3) and orthogonal to line L1:(5t – 1,3 –…

A: Consider the line L1given by the vector form: L1:5t-1, 3-2t, t    :-1+5t, 3-2t, 0+t    :-1, 3, 0+5t,…

Q: Find the equation of a plane through the point (1, – 1, 6) and orthogonal to the line x(t) = 7 + 4t…

A: Required plane is orthogonal to the given line, say L: x(t)=7+4ty(t)=-3-4tz(t)=-1-6t also, the plane…

Q: Find the distance between the line 2x - 3y + z = 6, 2y- z = 4, and the plane passing through the…

A:

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

A:

Q: 2. Find the plane that is orthogonal to the line : +1 = 431 = z and contains the point where l…

A: line parallel to the vector  V=⟨a,b,c⟩ passing through the point (x1,y1,z1) is given by the…

Q: Find the point of intersection of the line x-9 = - 5t, y +1= -t, and the plane 2x – 3y + 4z + 7 =0-…

A:

Q: find the trace of the plane in the given coordinate plane.  3x + 4z = −2, xy

A: To find the trace of the plane in the given coordinate plane  3x+4z=-2 --- (1) in the xy plane

Q: Find the equation of a plane that passes through the point (0,0,0) and contains the line x = 2 -t y…

A: Here we have to find the equation of a plane that passes through the point (0,0,0) and contains the…

Q: Find the equation of a plane that passes through the origin and contains the line x = 2t, y = 3t, z…

A: Consider the provided question, The equation of a plane passing through the point (x1, y1, z1) is…

Q: 1. Find the equation of the plane containing the lines L1 and L2 given below: z = 4t + 3 z = -4s – 1…

A: Given :L1:  x=2t+1, y=3t+2, z=4t+3L2 : x=s+2, y=2s+4, z=-4s-1

Q: Suppose we need to find an equation of the plane that passes through the line of intersection of the…

A: Since, we know that equation of a plane passing through the intersection of planes P and Q is given…

Q: Find an equation of a plane through the point (0,−2,1) which is orthogonal to the line…

A: The equation of a plane passing through the given point is as follows.

Q: b) Find the equation of the plane containing lines ₁ : x = 2+5t, y = 4+2t, z = -t and l₂: x=2-t₁y =…

A: We have to find the equation of the plane containing lines l1 : x=2+5t, y=4+2t, z=-t and l2 : x=2-t,…

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 point in which the line through the (3,-1,2) perpendicular to the plane x +2y -5 z = 4…

A:

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

A:

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

A:

Q: The planes 3x + 6z = 1 and 2x + 2y - z = 3 intersect in a line. Show that the planes are orthogonal.

A: Given: 3x+6z=12x+2y−z=3

Q: . Find symmetric equations of the line that is normal to the plane x-3y+2z =12 at the point where…

A: On the z-axis points are of the form (0,0,z)  We plug this in the given plane to find z So the line…

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

A: Remember that the vector (l, m, n) is parallel to the line with parametric equationx=a+lt, y=b+mt,…

Q: Determine an equation for the plane that passes through the point (1, 2, –3) and is parallel to the…

A:

Q: Find an equation of the plane that passes through the point (1,1,2) and contains the line x=3t, y=1,…

A:

Q: Find an equation of a plane containing the line r=⟨0,−5,−1⟩+t⟨−2,4,−2⟩ which is parallel to the…

A:

Q: Question 10

A: We have to find equation of plane that is parallel to the plane 6x-5y+8z+18 =0 and  the pale passes…

Q: Find an equation of the plane perpendicular to each of the planes z – y+z = 0 and 2r+y-4z–5 =0 and…

A: The given problem is to find the equation of plane perpendicular to each of the given planes and…

Q: Give an equation of the plane whose trace in the yz-plane has equation y = 6z, and in the xy-plane…

A:

Q: Does the line r(t) = intersect the plane 5x - 2y - z = 21 and if so, where?

A: