Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x = 2s + 2, y = s + 3, z = 5s + 6, and then find the plane determined by these lines.

### Want to see the full answer?

Check out a sample Q&A here*star_border*

## Related Calculus Q&A

Find answers to questions asked by students like you.

Q: Find the point of intersection of the lines x = 2t + 1, y = 3t + 2, z = 4t + 3, and x = s + 2, y =…

A: Click to see the answer

Q: Find the point of intersection of the lines x = 2t + 1, y = 3t + 2, z = 4t + 3, and x = s + 2, y =…

A: Click to see the answer

Q: Find the point of intersection of the lines x=2t+1,y=3t+2,z=4t+3,and x=s+2,y=2s+4,z=-4s-1 ,and then…

A: given lines are x=2t+1, y=3t+2, z=4t+3x=s+2,…

Q: Find the point of intersection of the lines x = 2t + 1, y = 3t + 2, z = 4t + 3, and x = s + 2, y =…

A: Equate the x and y coordinates in t and s domain to obtain values for t and s.

Q: Find the point of intersection of the lines 2t + 1, y = -t+ 2, z = t+ 1 and x 2s + 2, y = s+3,z =…

A: Given lines are x=2t+1, y=-t+2, z=t+1x=2s+2, y=s+3, z=5s+6

Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x = 2s + 2, y = s + 3,…

A: Click to see the answer

Q: Find the plane that contains the point (0, 1, 2) and the line x = 1- t,y = 2 + t,z = 4 + 3t.

A: Here I am attaching image so that you understand each and every step.

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

A: If normal vector is <a, b, c> Then equation of plane perpendicular to line with normal vector…

*question_answer*

Q: .) Find the plane which contains both lines: a. x = 1-4t, y = 1+2t, z = 2-2t b. x = -1+s, y = 2+s, z…

A: Since you posted here 3 questions, I can answer only first one. Please reupload remaining two…

*question_answer*

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…

*question_answer*

Q: Find the distance between two lines (L1: x=3t-1, y=t+6, z=2t+3 and L2: x=2t+6, y=2t+11, z=-t+3)…

A: Click to see the answer

*question_answer*

Q: Find the point of intersection of the lines x t, y = -t + 2, z = t + 1, and x 2s + 2, y s + 3, z 5s…

A: Click to see the answer

*question_answer*

Q: Find the plane determined by the nterseetieg Lines L X=1-2t, , 31-3t,,そニ-2+t, LX--3+ti,…

A: Click to see the answer

*question_answer*

Q: Find the plane containing the intersecting lines x = -1+t, y = 2+ t, z =1–t; -0 <t < o∞ | L2: x = 1…

A: Find the planes containing the intersecting lines: L1:x=-1+t,y=2+t,z=1-t for all…

*question_answer*

Q: Find the line r that passes through the origin and is perpendicular to the π planes that passes…

A: Click to see the answer

*question_answer*

Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with .the xy-plane,…

A: In xy plane : z = 0 means t = 3, so the point of intersection is (-2,10,0). Similarly.

*question_answer*

Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with the xy-plane,…

A: Given, The line x = -2, y = 4+2t , z = -3+t We have to find the points of intersection of line…

*question_answer*

Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with .the xy-plane,…

A: In xy plane z = 0 = t - 3. Therefore t = 3 so the point of intersection is (-2,10,0). Similarly.

*question_answer*

Q: Determine if the plane given by -x + 2z 10 and the line given by %3D (x = 5, y = 2 -t,z = 10 + 4t)…

A: given plane: -x+2z+10 given line: (5,2-t,10+4t)

*question_answer*

Q: Find the distance between two lines (L1: x=3t-1, y=t+6, z=2t+3 and L2: x=2t+6, y=2t+11, z=-t+3)…

A: Click to see the answer

*question_answer*

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.

*question_answer*

Q: Find the equation of the plane containing the line: x = 2 + 10t, y = 2 – 2t, z = 9 + 4t and parallel…

A: Click to see the answer

*question_answer*

Q: find the plane containing the intersecting lines. L1: x = t, y = 3 - 3t, z = -2 - t; -inf < t…

A: This question is taken from the planes in which we have to find the plane equation. We can write the…

*question_answer*

Q: Find the point at which the line intersects the given plane. x = 3 - 3t, y = 4t, z = 1 + t; x + 2y -…

A: Given line ,x=3-3ty=4tz=1+t -1and plane , x+2y-z=6

*question_answer*

Q: Find a plane containing the line r(t)=+t and orthogonal to the plane −7x−6y+3z=2

A: Click to see the answer

*question_answer*

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

A: Click to see the answer

*question_answer*

Q: Find equation of the plane that contains the lines L1:x = 3 + 5t, y = 6+ 2t, z = 6 + 3t and L2: x =…

A: Equation of plane which passes through L1 is ax-3+by-6+cz-6=0 where 5a+2b+3c=0.

*question_answer*

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

A: Here the two equation are: x+2y+z=1x+y+2z=-1

*question_answer*

Q: Find the intersections of the line x = -2, y = 4 + 2t, z = -3 + t with the xy-plane, the xz-plane,…

A: Click to see the answer

*question_answer*

Q: Consider the line which passes through the point P(1, -3, -2), and x = 1+4t, y =2+7t, z 3+ 1t Find…

A: Click to see the answer

*question_answer*

Q: Check that the line (1,0,1)+t(3,0,1) is parallel to the plane -2x+4y+3z=13 and calculate the…

A: For the equation of the plane , the direction vector of the normal to the plane is given by . For…

*question_answer*

Q: Show that the plane 2x − y − 3z = 4 is parallel to the line x = −2 + 2t, y = −1 + 4t, z = 4, and…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

*question_answer*

Q: Find equation of the plane that contains the lines L,:x 3+5t, y = 6+2t, z = 7t and L2: x = 7t, y =…

A: Click to see the answer

*question_answer*

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

*question_answer*

Q: Determine the general equation of the plane containing the point (1, 2, –1) and the line

A: The given equation of the line- 1-x3=y+23=z-3 It can also be written as follows- x-1-3=y+23=z-31…

*question_answer*

Q: Find the point at which the line intersects the given plane. x = 4 - t, y = 5 + t, z = 3t; x - y +…

A: Click to see the answer

*question_answer*

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

A: Click to see the answer

*question_answer*

Q: Find an equation for the plane parallel to the line x = 1 − 2t, y = 2 + 3t z = 1 + 2t and that…

A: Click to see the answer

*question_answer*

Q: Find an equation of the plane containing (1, 5, -1) that is perpendicular to the line of…

A: Click to see the answer

*question_answer*

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

*question_answer*

Q: Find a plane containing the line ī(t) = +t and orthogonal to the plane 5x – 6y – 7z = - 5

A: We have find the equation of plane containing the line r→(t)=⟨-7,3,5⟩+t⟨4,8,-8⟩ and orthogonal to…

*question_answer*

Q: Find the distance between the point (0, 1, 2) and the plane 3x - 2y + 6z = 6.

A: Using Distance from point to plane formula,

*question_answer*

Q: Find an equation of the plane that passes through the point (1,2,3) and which is orthogonal to the…

A: Click to see the answer

*question_answer*

Q: Is the line x = 9- 8t, y= 4 + 2t, z= - 5t parallel to the plane 2x + y-z=2? Give reasons for your…

A: Click to see the answer

*question_answer*

Q: Determine whether the line L : x = 3 – 4t, y= 5+2t, z = 5 + 4t, - is parallel to the plane x - y +…

A: Click to see the answer

*question_answer*

Q: If the line L: X = 3 + 2t , Y= 2t , Z=t intersects the plane X+ 3y Z -4 in a point P. The…

A: Click to see the answer

*question_answer*

Q: Let L, be the line through the points (1,2,6) and (2,4,8). And let L2 be the line of intersection of…

A: Click to see the answer

*question_answer*

Q: Find a plane through the points P1(1, 2, 3), P2(3, 2, 1) and perpendicular to the plane 4x − y + 2z…

A: Click to see the answer

*question_answer*

Q: Find an equation for the plane parallel to – 2x + 9y – 2z 30 and containing the point (1, 4, 3)

A: Click to see the answer