Q1: Two lines in space {x 1- 2t,y 2 +3t,z =-1+t} and {x = 1+t,y% 3+ 2t,z = -1+3t} find the angle between the them, then find the parametric equation of the plane containing the two lines.

Q: Find parametric equations for the line through (-2,0,4) parallel to V=2i +4j -2k .

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Q: a) Find the best straight line fit to the given data points (-3,7), (1,–1),and (3,–7). b) Find the…

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Q: Find the parametric equations for the line through the point of intersection of the lines L,:x = 2…

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Q: Find parametric equation for the lines .. The line through (0, -7, 0) perpendicular to the plane x +…

A: A parametric equation of a line can be written if a point on the line is given and a vector parallel…

Q: Complete the parametric equations for the line where the planes - 5x – 2y + 2z = 2 and - 13x + 10y +…

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Q: oblem 20. Does the line with parametric equation x = 21 + 1, y = 3t- 2, z = 2t – 2, 1 e R intersect…

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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: 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: Eliminate the parameter in the parametric equations x(t) = -6t + 8 and y(t) the equations. = 30t –…

A: givenx=-6t+8....................(i)and y=30t-10...................(ii)x=-6t+86t=8-xt=8-x6

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

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Q: Find parametric equations of the line through (-3,0,9) that is parallel to 2i-6j+k. x(t)= 11 y(t) =…

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

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Q: 1: Find the angle between the planes 3x - 6y + 4z 3 and 2x - 2y +z = 4 then find the parametric…

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Q: Q3/ Find the real number such that the line of parametric equations x = t, y = 2 - t, z= 3+t, is ax…

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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: Find parametric equations for the line segment joining the points (9, 8) and (16, 11). O x=9+7t, y…

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Q: 8. The position of a particle moving in the xy-plane is given by the parametric equations x =…

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Q: What does the graph of the parametric equations x (t) = 2-t and y(t) = (t + 3)², where t is on the…

A: Given parametric equation:x(t)=2-ty(t)=(t+3)2 where t is on the interval  [-4, 0]

Q: Find the angle between the two planes 3x + 2y − z = 7,  x − 4y + 2z = 0 and find a set of parametric…

A: Known fact: The angle between two planes a1x+b1y+c1z+d1=0  and a2x+b2y+c2z+d2=0 is given by…

Q: Consider two non-parallel lines , l1 & l2, in R³ with parametric equations l1: P+ tu l2: Q + tv.…

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Q: Given the planes  π1 : x − 2y + 3z + 1 = 0 and π2 : 2x + y + z + 2 = 0. Let L be the line of…

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Q: The parametric equations x = 16+ ² + St. Y= 4+³+3+² ned come correspond to the Do Not make…

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Q: 2. Find the point(s) of intersection of the following two parametric curves, by first eliminating…

A: From x=t+5 we get t=x-5 Then we plug this in the y=t2 So, the equation is: y=(x-5)2   We can plug…

Q: Q2:- Find the parametric equations for the following Cartesian equations. 1) x=(/y² + 4 + 2) 2) 4x2…

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Q: Find the point P of intersection between the line x(t) = (-3,-2, 1) + t (1, 1, -3) and the plane 4z…

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Q: Find the parametric equations for the line through the point of intersection of the lines L1:x = 2 +…

A: In line L1 and L2  't' is used as parameter but don't confuse with it. Different different line we…

Q: Find parametric equations for the line through P0 = (3, −1, 1) perpendicular to the plane 3x + 5y −…

A: A line L in sace with direction vector d=d1,d2,d3 that asses throughthe point P=(x0,y0,z0) can be…

Q: 1. Eliminate the parameter to find a Cartesian equation of the curve with parametric equations z =…

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Q: Find the point at which the line given by the parametric equations below intersects the plane.…

A: Given a system of linear equations are, 2X + 4Y -3Z =-48.................(1) X = 10 +…

Q: d) Find the parametric equations for the line of intersection of the two planes.

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Q: Find the angle between the two planes x- 2y + z = 29, 2x + 3y – 2z = 6. And also find the parametric…

A: here we will find angle between two planes and parametric equation of plane's line of intersection,

Q: Find the parametric equation for the line where the planes 4x – by + 8z = - 36 and – by + z = – 15…

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Q: Find parametric equations for the lines in The line through (0, -7, 0) perpendicular to the plane x…

A: we know that equation of line in parametric form which passes through pointx1,y1,z1 and…

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

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

A: C : x = 5 + z        y  = 3z^2

Q: Find the distance between the skew lines with parametric equations x = 3 + t, y = 1 + 6t, z = 2t,…

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

Q: Complete the parametric equations for the line where the planes - 7x + y + 3x = 3 and 4x7y + z = 23…

A: Given two planes -7x+y+3z=3 and 4x-7y+z=23

Q: Given the planes 3.x – 6y – 2z = 15 and 2x + y – 2z = 5 anser the following. (b) Find parametric…

A: I have solved using an intersection point and direction ratios

Q: Q.1 Find the parametric equation of the line that 2)Passes point (1,3,7) and orthogonal to xy-…

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Q: Find parametric equations of the line through (-2, –1, 3) that is parallel to 2i – 3j+k. x(t) = %3D…

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Q: Find parametric equations for the line through (- 3,1,2) perpendicular to the plane 7x + 9y + 9z =…

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Q: Find the parametric equation for the line where the planes 4x – 6y + 8z = - 36 and – 6y + z = – 15…

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Q: Complete the parametric equations for the line where the planes -4x + 2y – 14z = – 32 and -x – y –…

A: Use parametric equation of tangent line

Q: 6. a. Find the length of the curve using the equation 12xy = 4x4 +3, from x = 1 to x = 3. b.…

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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…

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Q: Q5) Find the angle between the plane x+y-z=3 and the plane that perpendicular to the line has the…

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Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 2x + y…

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Q: 5. Find parametric equations for the line of intersection of the planes x + y = 1 and y +z = 1.

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Q: Find two different sets of parametric equations for the rectangular equation  y = 4x + 1, t = −1 at…

A: Given equation is y=4x+1, t=-1 and the point is (-2,-7).

Q: Eliminate the parameter in the parametric equations x(t) = –7t – 2 and y(t) = Vt – 8 to find a…

A: givenx(t)=-7t-2..................(i)y(t)=t-8..................(ii)we can rewrite 2nd equation…