8. Find a parametric representation of the line through the point P(1,0,4) and perpendicular to the plane given by 2x – y + 3z= 18.

Q: What is the parametric equation of line through the point (1,2, -1) and perpendicular to the plane…

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Q: 2 7 Find the projection of v = -1 onto the line tlof R'Igiven by the parametric equation e = tul…

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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 a set of parametric equations for the line passing through the point (2, 0, 9) that is…

A: a set of parametric equations for the line passing through the point (2, 0, 9)  that is parallel to…

Q: 33 and Complete the parametric equations for the line where the planes – 3x – 9y – 12z = - 11x + 2y…

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Q: 12- Find an equation of the tangent plane to the given parametric surface at the specified point.…

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

A: Given surfaces are And the given point P is

Q: 3. Find a set of parametric equations for the line of the intersection of the planes 3x-3y-7z -4 and…

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Q: Find a parametric equation for the line through the point(1,9,3) and perpendicular to the plwne…

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Q: Find a parametric form for the line through the point (8, –6, –3) and perpendicular to the plane 2x…

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Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

A: What is the parametric equations of line line through the point (1,2,-1)and is perpendicular to the…

Q: 4. Determine the parametric equation of the line that passes through (2, -1, 3) and is perpendicular…

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Q: Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?

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

A: We need to obtain a set of parametric equations for the curve of intersections of the cylinders:…

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: Consider the planes 71 : x - 2y + 3z +1 = 0 and 72 : 2x + y+z+2 = 0. Let l be the line of…

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Q: 5. Find the distance from the point (3, 0, 10) to the plane 2x+3y+ z = 2. 6. Write the parametric…

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Q: s) Find the parametric equations of the line that is perpendicular to the plane 2x +y+3z = 4 through…

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Q: What are the parametric equations for the intersection of the planes x - y - z = 1 and 2x + 3y + z…

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Q: Find the parametric equations for the line through the point (5, 2, 9) and perpendicular to the…

A: The parametric equation of a line passing through the point and has a direction cosines <a , b…

Q: The parametric equation for the line passing through P(1,1,5) and parallel to n=(0,0,1) is defined…

A: Topic = Vector

Q: Complete the parametric equations for the line where the planes 8x + 11y + 4z 13x + 2y + 3z = 5…

A: This question can be solved using the concept of lines and planes in three dimensional geometry.

Q: Find an equation of the plane in standard form (ax + by + cz = d) that passes through the point (4,…

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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: 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: 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: 6. Find parametric equations for the line of intersection of the planes 2x – y + z = 4 and 3x + y +…

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

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Q: Find an equation of the line through (0,0,0) that is parallel to the e parametric equations x(t) = 2…

A: To find out equation of any line we need one point on the line and a vector which is parallel to the…

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

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Q: Match the parametric equation with the corresponding plane curve displayed. Sx=47-5 y=16 130 104 78…

A: The given parametric equation is: x=4t2-5y=16t4

Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y z 1…

A: Given:

Q: Find parametric equations for the line through (- 4,6,1) perpendicular to the plane 7x + 3y + 9z =…

A: Note that, a vector which is perpendicular to the plane ax+by+cz+d=0 is (a, b, c). A parametric…

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

A:

Q: Find parametric equations for the line in which the planes x + 2y + z = 1 and x - y + 2z =-8…

A: x + 2y + z = 1 and x - y + 2z =-8 are the two planes.Let z=t So, the equations become:

Q: Compute the parametric equations of the line in R3 determined by the intersection of the two planes:…

A: To obtain the parametric equations of the intersection line, use the following formulae. Let n1→…

Q: Eliminate the parameter in x = -t +2t and y =t-4 and then identify the parametric curve and sketch…

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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: 9) Find a parameterization of the line formed by the intersection of the following planes: P,: 2x -…

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Q: # 2. Let C be the curve that is the intersection of the cylinder x²-2x+4y2 = 0 with the plane z-x…

A: The cylinder x2-2x+4y2=1 and a plane z-x=3. We have to find the parametric equations for the…

Q: a) Prove that the lines with parametric equations: x = 1+ t, y = 1 + 6t, z = 2t and x = 1+ 2s, y = 5…

A: Given that: Line L1:  x=1+t, y=1+6t, z=2tLine L2:  x=1+2s, y=5+15s, z=-2+6s

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

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Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y² = 8 ,…

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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: Derive the parametric equations of the line of intersection of the two planes: II : x – 2y + z =1…

A: Given: P1:   x−2y+z=1P2:   2x−2y−4z=4