35. DISCOVER: Intersection of a Line and a Plane A line has parametric equations y = 3t 2= 5 - 1 x = 2 + 1 and a plane has equation 5x – 2y – 2: = 1. (a) For what value of t does the corresponding point on the line intersect the plane? (b) At what point do the line and the plane intersect?

Q: Find parametric equations for the line through the point P(3, 6, 4) that is parallel to the plane x…

A:

Q: ) Find the parametric equations for the line through the point P = (-2, 5, -3) that is perpendicular…

A: topic - equation of a line through given point and perpendicular to a plane

Q: Find parametric equations for the line through Po= (3, -1, 1) perpendicular to the plane 3x + 5 y -…

A: Given:  a Point Po =(3, -1, 1)  and a vector perpendicular to the plane is…

Q: b) Given two planes 71 : 2x – 4y + z = 5 and T2 : 7x + y – 2z = 14. i. Find the acute angle between…

A: We will find the angle and the equation of line as following.

Q: Q/ Find the parametric equation for the line through the point (0, 1, 2) that is perpendicular to…

A:

Q: Find parametric equations for the line formed by the intersection of planes x + y - z = 29 and 3x -…

A: Consider the given:…

Q: Q1. The parametric equations of the lines L1, and L2 are given as: L: x=-2+1, y=3+2t, z=-t+4 L₂:…

A: Let's find distance between two lines.

Q: 0 M) Find the point at which the line with parametric equations X=2+31, y=-41, z z =5+1 intersect…

A: Given:         x=2+3t         y=-4t         z=5+t    plane  4x+5y-2z=18

Q: Find parametric equations for the line through Po = (3, –1, 1) perpendicular to the plane 8x + 5y –…

A:

Q: 31. (a) Show that the parametric equations x = x, + (x2 – x1)t y = yı + (y2 – yı)t where 0 <t< 1,…

A: Given data: The first parametric equation is x=x1+(x2-x1)t. The second parametric equation is…

Q: Find the parametric equations of the intersection of the planes x + (y - 3) + z = 0 and -x + (y + 3)…

A:

Q: Find parametric equations for the intersection of the planes 2x + y − 3z = 0 and x + y = 1

A: Two planes lying in 3-Dimensional plane can intersect each other at any point and that point can lie…

Q: A particle starts at the point P = (-6,5, -3) and moves along a straight line toward Q - (-4, 8, -1)…

A: Given :  P=(-6, 5,-3)  Q=(-4, 8,-1)  To find: parametric equations and Velocity

Q: Find parametric equations for the line through the point (0, 2, 3) that is perpendicular to the line…

A:

Q: a) Find parametric equation for the line of intersection of T1 : x + 2y – z +1 = 0 and TT2 : 2x – y…

A:

Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4…

A: This is the problem from the vector algebra and 3D geometry.

Q: 1. Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the…

A:

Q: (a) Find parametric equations for the portion of the cylinder x² + y² = 5 that extends between the…

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

Q: 8) Find the parametric equation of the Line passes through p (2 -4,5) parallel 19to 3x+y-97 =5 and…

A: This question can be solved using the concepts: general equation of a line condition of  line and…

Q: Find a parametric equation for the line through the point (2,3, – 1) and perpendicular to the plane…

A: Given that The point on the line (2,3,-1) and perpendicular to the plane 8x+3y+3z=5 A vector…

Q: 24. Match the graphs of the parametric equations x = f(f) and y= g(t) in (a)-(d) with the parametric…

A: This question is related to parametric equations and graphs, we will solve it using given…

Q: 18. Find the acute angle between the plane x+2y-z=8 and the line with parametric equations x =1, y…

A:

Q: A line with parametric equations x = 10 + 2s, y = 5 + s, z = 2, seR, intersects a sphere with the…

A: The solution of given problem as follows :

Q: 4. Find the parametric equation of the line through (1, 0, -2) and parallel to the line % (x – 4) =…

A: This is the answer of question no. 4.

Q: Find a set of parametric equations for the line passing through the point (2, 0, 4) that is parallel…

A: To find a set of parametric equations for the line passing through the point 2, 0, 4 that is…

Q: nd a set of parametric equations for the line passing through the point (1, 0, 9) that is parallel…

A:

Q: Find parametric equations for the line through the point  (0, 2, 2)  that is perpendicular to the…

A:

Q: Find the parametric equations for the line through the point (1, 7, 2) that is parallel to the plane…

A:

Q: 24) Consider line L of parametric equations x =t, y = 2t, z = 3, t E R. a. Find parametric equations…

A: The given line is: x=t, y=2t, z=3 and t∈R Now, consider the angle θ between two intersecting plane,…

Q: 1. The Cartesian equation of the curve given in parametric equations x = et - e-t , y = e' + et is…

A: As per guideline we have to do only one question

Q: If x = 1- 2t and y = 1+t denotes the parametric equation of a line in 2D , then (-2,1) is a) A point…

A:

Q: O Given two points P(6,3,1) and Q(5, 0,0), find the parametric equations for a smooth curve, C:x =…

A:

Q: Find parametric equations for the line through Po = (3, -1, 1) perpendicular to the plane 8x + 5y –…

A: Consider the point Po and the equation of the given plane. Find the vector Po and the direction…

Q: d a set of parametric equations for the tangent line to the curve of intersection of the surfaces at…

A: Given surfaces are z=x2+y2 and z=16-y at the point 4,-1,17. To find a set of parametric equations…

Q: 3. What is the parametric equation for the line through the point (1,2,3) parallel to the y - axis?…

A: The solution is given as follows

Q: Find the distance between the skew lines with the given parametric equations. x = 2 + t, y = 3 + 6t,…

A:

Q: I Let C be the line segment from A(0,-3) to B(-4, 1). a) Sketch the graph of C, and find parametric…

A: The parametric equation of a line includes a real parameter t. It is of the form  x=xt,y=yt A line…

Q: Find the parametric equations for the line of intersection of the planes x+y+z= 3 and 2:z-3y = 6.…

A:

Q: (a) Find parametric equations for the line through (5, 2, 4) that is perpendicular to the plane x -…

A: answer is in next step.

Q: (A) Find the parametric equations for the line through the point P = (-3, 4, -2) that is…

A: the parametric equation of a line passing through the point (x1,y1,z1) and  having direction ratio…

Q: 2x-y-z 4 and b: *+リーニ=2 - Given the non-intersecting lines a: x-2y+z=1 x+y+z 1 Find the line that…

A:

Q: Find a set of parametric equations for the line passing through the point (1, 0, 2) that is parallel…

A:

Q: Determine any differences between the curves of the parametric equations. (a) x = t y = 9t + 8 (b) x…

A:

Q: It can be shown that the parametric equations I = x1 + (x2 – r1)t, y = Y1 + (y2 – Y1)t, where 0 < t…

A:

Q: Q. Find parametric equation of the line perpendicular to the lines l1: x = 1- 1, y=t, 12 : z = 2t –1…

A:

Q: (3) Find parametric equations for the line of intersection of the planes. x + y - z = 2 and y + z =…

A: Given equation of the planes are  x+y-z=2     y+z=0 we rewrite them as x+y-z-2=0, and    0x+y+z=0…

Q: I am completely lost on this one. Find parametric equations for the line through the point (0, 1,…

A: Find parametric equations for the line through the point (0, 1, 2) that is perpendicular to the line…

Q: find parametric equations for the line tangent tothe curve of intersection of the surfaces at the…

A: Given surfaces, x2+2y+2z=4     and   y=1f(x,y,z)=x2+2y+2z-4          and   f(x,y,z)=y-1  And point…

Q: Find a set of parametric equations for the curve of intersection of the cylinder (x - 1)2 + y2/4 = 1…

A: