Find the distance between the point (4, −1, 5) and the line given by the set of parametric equations ; x = 3, y = 1 + 3t, z = 1 + t

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

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Q: Eliminate the parameter from the parametric equations to find the rectangular equation for the…

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Q: Find the angle between the two planes 6x − 3y + z = 5,  −x + y + 5z = 5 and find a set of parametric…

A: We have given the equation of planes; 6x − 3y + z = 5 −x + y + 5z = 5 Hence the normal vectors of…

Q: Find a set of parametric equations for the rectangular equation that satisfies the given condition.…

A: Given :                y = 2 x - 5  ,  t = 0        at point (3,1)

Q: Write an equation in general form of the tangent plane to the parametric surface at the stated…

A: Equation of tangent plane

Q: Complete the parametric equations of the line through the point (-6,0,-8) and perpendicular to the…

A:

Q: Find parametric equations for the line segment joining the points (5, 3) and (11, 11). x=t, y = 3 +…

A: Solution

Q: Describe the relationship between the lines with the following parametric equations: x = 1- 41, y =…

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Q: find the parametric equations of the line through (-3,0,2) that is parallel to 3i-4j+k. x(t)= y(t)=…

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Q: A parametric equation of the line of the intersection of the planes x - z = 0 and x – y + 2z = 0 is

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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 parametric equations for the line segment joining the points (6, 2) and (9, 10). x=t, y 2+8t,…

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Q: Find parametric equations of the line through (-1, –1, 6) that is parallel to 2i – 4j+k. x(t) = y(t)…

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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: Find parametric equations of the line through (-3,0, 4) that is parallel to 5i– 8j+k. x(t) y(t) =…

A: Parametric equations of a line passing through the point P(a,b,c) and parallel to the vector v→=…

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: The parametric equation of the line through the origin that is parallel to the line given by x = t,…

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Q: Complete the parametric equations of the line through the point (6,-6,8) and perpendicular to the…

A: Line passing through the point 6, -6, 8 and perpendicular to the plane 7x+2y-3z=-8. Since the line…

Q: 4. Find the equation of the plane that passes through the point (5, –1,0), and is per- pendicular to…

A: Let's find.

Q: x = 12 + 3 y = 2t [-2, 2]

A: Substitute t value

Q: Find the (perpendicular) distance from the line given by the parametric equations æ(t) 3 – 4t %3D…

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Q: Without eliminating the parameter t, find a Cartesian equation for the lin curve C, defined by the…

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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: Find the angle between the two planes −2x + y + z = 2,  6x − 3y + 2z = 4 and find a set of…

A: The given planes are −2x + y + z = 2  and  6x − 3y + 2z = 4 . Obtain the angle between them as…

Q: Complete the parametric equations for the line where the planes – 8z – 2y – 5z = 0 and - 4x + 2y –…

A: Given: The planes are -8x-2y-5z=0 and -4x+2y-9z=0 To find the parametric equation xt, yt, zt

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A: Let's find.

Q: Given the curve of intersection of the x² + 4y² -z = 0 which is a paraboloid and the plane 2x - z =…

A: Solution:-

Q: Find the general equation of the plane through the point (1, 1, 1) that is perpendicular to the line…

A: We know that equation of plane which passes through pointx1,y1,z1 and perpendicular to linex=x2+at,…

Q: Find parametric equations, in terms of t, of the line passing through (2, 2, 12) and parallel to the…

A: Given: The line is passing through 2,2,12. Also, it is parallel to the line: x=5-9ty=2z=4+t The…

Q: Find a set of parametric equations for the curve of intersection of the paraboloid r² + 4y² -z = 0…

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Q: Find the angle between the two planes 3x − y + z = 7 ,  4x + 6y + 3z = 2 and find a set of…

A: Given, two planes 3x − y + z = 7 ,  4x + 6y + 3z = 2  we have to find the angle between the two…

Q: Find parametric equations for the line segment joining the points (-6, 4) and (2, 3). x=-6 + 8t, y =…

A: Parametric equation of line segment.

Q: Find the distance between the point (2, 3, 2) and the line given by the set of parametric equations…

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Q: Sketch the plane curve represented by the parametric equations x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π…

A: Given  x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π

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

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Q: Find the length of the parametric curve x = 2t + 1, y = 3 + 2tž, 0 < t <%.

A: Find the Length of the curve

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: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² − z = 0…

A: To find the parametric equations for the intersection of given surfaces.

Q: Sketch the plane curve represented by the parametric equations x = Vi and y = }t + 1 by eliminating…

A: The parametric equations are given by x=t   …1 and y=12t+1   …2 Take the square of the equation (1)…

Q: Find the distance between the point and the line given by the set of parametric equations. (Round…

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Q: Find the distance between the point and the line given by the set of parametric equations. (Round…

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Q: Find the (perpendicular) distance from the line given by the parametric equations ¤(t) -2 – 2t y(t)…

A: Solution: The objective is to find the perpendicular distance

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: Sketch the plane curve represented by the parametric equations x = 5 cos t, y = 2 sin t, 0 ≤ t ≤ π…

A: x=5cost,  y=2sint Now,…

Q: Find a set of parametric equations for the rectangular equation that s y = 2x – 3, t = 0 at the…

A: let x = t + a put all the given points to find out the value if a x = 4 and t = 0 4 = 0 + a a = 4 so…

Q: Find the parametric equations for the line of the intersection L of the two planes. 6x – 3y+ z = 5…

A: Parametric equations of the line is :  x(t) = x0 + a t  y(t) = y0 + b t  z(t) = z0 + c t  Here ( x0…

Q: Find the distance between the point and the line given by the set of parametric equations. (Round…

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Q: Eliminate the parameter to find a Cartesian equation of the curve with parametric equations x = et –…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.