6. Find the distance between the point (- 3, 2, 1) and the line with parametric equations x = 3 – 2t, y =1-t, z = -3t

Q: parametric

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Q: Find a set of parametric equation of the line through the point (1, 0, 1) parallel to the line x = 3…

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

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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)

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A: To find out the equation of the plane tangent to the elliptic paraboloid.

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Q: 8. Find a parametric representation of the line through the point P(1,0,4) and perpendicular to the…

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Q: Find the set of parametric equations of the line through the point (1, 6, 3) that is parallel to the…

A: The direction ratio of the line x=6+5t, y=6+2t, z=4+2t is (5,2,2). Parallel lines have the same…

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

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Q: I am working with cal 3. How do I find the parametric equations of the line for the intersection of…

A: The parametric equations of a line through the point (x0, y0, z0) and parallel to the direction…

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

A: Explanation: Given that,  Line 1: x=1+ty=1+6tz=2t Vector 1: 1,6,2 Line 2: x=1+2sy=5+15sz=-2+6s…

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

A: The objective is to find the parametric equations of the line through the point.

Q: Graph the curve with parametric equations x = sin(t), y = 3 sin(2t), z = sin(3t). H0.0 y -0.5 0.5…

A: The graph will look like this:

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

A: We have to find parametric equation for the line that is perpendicular to the graph of the given…

Q: Find the distance from the point (3, 2, 5)to the line with parametric equations x=t,y =l +t ,z = 2 +…

A: The equation of the line in matrix form:                                                xyz = 012 +…

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A: Any point in three dimensional coordinate system will be of the form x1,y1,z1 . We can calculate the…

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Q: 4. Find the equation of the tangent plane at the point (-2, 1, -3) to the ellipsoid 22 + y? + = 3 4

A:

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

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

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

A: The solution is given below in the next step:

Q: I need to get the parametric equation for a line between the points (0,1,2) to (3,0,-1). I have the…

A: Line passing though the points 0, 1, 2 & 3, 0, -1. Now let, x0, y0, z0=0, 1, 2 & x1, y1,…

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Q: y+3x-6z=8

A: answer is in next step

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

A:

Q: Find parametric equations for the line formed by the intersection of planes x+y-z=3 and 3x-y+3z=5.

A: First we find a point on the intersection of these planes with the plane z=0. And next find the…

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Q: 2. Find an equation of the tangent plane to the parametric surface F(u, v) = (, 2uv, uv?) at the…

A: (2) Consider the provided question,

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> +…

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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: If I have a pair of parametric equations  x=20cos(t) and y=10sin(t)  How can I increase the speed…

A: