(a) Prove that the lines with parametric equations: x = 1+t, y = 1+ 6t, z = 2t and x = 1+ 2s, y = 5 + 15s, z = -2 + 6s are skew. (b) Find the distance between the two lines.

Q: B- Find the parametric equations for the line through point (1,0) and parallel to the function f(x,…

A:

Q: Find parametric equations for the line in which the planes, x+2y-2z=5 and 5x-2y-z=0 intersects. Show…

A: Given, The equation of intersecting planes, x+2y-2z=5 and 5x-2y-z=0.   We have, x + 2y = 2z + 5 and…

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

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Q: 1) Find the parametric equations of the line that is tangent to circle x² + y2 = 25 %3D at point (3,…

A: Given: Equation of circle: x2+y2=25 and tangent at point 3, -4

Q: Find parametric equations of the line through (-1,0,3) that is parallel to 5i – 6j+k. x(t) y(t) =…

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Q: The parametric equation of the line resulted from intersection of x-y 0, and z = 2 is %3D

A: Use the given planes.

Q: Find parametric equations of the line through (-1,0,1) that is parallel to 2i – 6 j+ k. -

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Q: Find the parametric equation of the line that passes through P(-2, 0, 3) and is parallel to the line…

A: Given that: Equation of line is:     x=-1+3t, y=2-2t, z=3+t  and the point is : P(-2, 0, 3)

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 the distance between the point (1, −2, 4) and the line given by the set of parametric equations…

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

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

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Q: How do you find the parametric and symmetric equation of the line passing through the point (3, 2,…

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

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Q: Find the parametric equations for the line in which the planes x-2y+4z=2 and x+2y-2z=6 intersects

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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: Find a parametric equation for the line through the point (6,5, - 3) and perpendicular to the plane…

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Q: find a parametric equation for the line that is perpendicularto the graph of the given equation at…

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

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

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Q: ) (i) Find the parametric equations for a smooth curve, C: x= 4z, y = -3z that joins two points,…

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Q: Find a set of parametric and symmetric equations of the line satisfying the following Passing…

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

Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 2x + 4y +…

A: Equation of line normal to graph of functions f(x) is :  r<t> = <x0,y0,z0> +…

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

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

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

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Q: Find the parametric equations of the line segment through the origin and perpendicular to the plane…

A: Given: Given equation of the plane is x-2y+3z=5 We want to find the parametric equations of the line…

Q: 30. Determine two sets of parametric equations for the line passing through the points P( 1,7, 1)…

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Q: Find parametric equations for the line pass- ng through the point P(1, –1, 3) and perpen- licular to…

A: Given that: Line is passing through P(1,-1,3) and perpendicular to the plane:       4x+3y-2z=6.

Q: Find parametric equations for the line in which the planes, X+2y-2z=5 and 5x-2y-z=0 intersects. Show…

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Q: Find the parametric equation of the intersection of the planes x + y = 1 and x + z = 2.

A: Equation of plane 1 - x+y = 1        Normal vector of plane 1 = n1 = 1,1,0…

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

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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 a parametric equation for the line that is perpendicular to the graph of the equation 4x+2y…

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

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Q: 6. Find the distance between the point (- 3, 2, 1) and the line with parametric equations x = 3 –…

A: Consider a point on the line (3-2t, 1-t, -3t) which is the foot of the perpendicular to the point…

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Q: Find the distance between the point (4, −1, 5) and the line given by the set of parametric equations…

A: The point is: P(4, −1, 5) The line is: x = 3, y = 1 + 3t, z = 1 + t The line is: <3, 1, 1> +…

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

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Q: The angle and the parametric equations for the intersect line between planes x + y = 1, and 2x + y–…

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Q: Find the distance between point A(3, 4, 4) and the line of parametric equations x = -1-t, y = -t, z…

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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