4. (a) Find a parametric equation and symmetric equation of the line that pases through the point (2, –1,3) and is parallel to the vector 7 +27 – 3k. (b) At what points does this line intersect the yz-plane?

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

A:

Q: Give a vector parametric equation for the line through the point (3, 1) that is perpendicular to the…

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Q: 1. What is the vector and parametric forms of the equation of the line passing through points…

A: This question can be solved using the concept of vector and parametric equation of line passing…

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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: 4. Find parametric equations of a line passing through (1, 2, 3) that is parallel to the plane…

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A: Question 17 In general, we know that the equation of the line passing through the point (x1, y1, z1)…

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Q: Find the vector parametric equations of the two straight lines tangent to the given space curve

A: Given,              rt=2t2+3i+15t-7j+4t2+5kand  passing through the point P-3, -22, -7.

Q: Find parametric equations for the line described below. The line through the point P(1, 1, -2)…

A: we have to find

Q: Find an equation of the plane through the point (2,1,-3) with normal vector 2i-3j+k. Determine the…

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Q: Find a set of parametric equation of the line through the point (-2, 0, 3) parallel to the vector v…

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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 the parametric equations for the line in which the planes -4x +y+3= = 5 and 2x+y+ = 3…

A: Given that:-4x+y+3z=5    .............(1)2x+y+z=3          ..............(2)

Q: a b 3. Write the scalar equation of the plane with normal vector = [5,-1,-2] and passing through the…

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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: Find the parametric equations for the line in the x-y plane which goes through the points (2,-1) and…

A: The parametric equations for the line in the x-y plane which goes through the points (2,-1) and…

Q: Find the parametric equation for the line in R' that passes through the point (1, –2, 3) and that is…

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Q: Find a set of parametric equations for the line passing through the point (8, 0, 9) that is parallel…

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

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Q: Find parametric equations for the line through the point P(2, - 5, - 3) parallel to the vector 31 -…

A: topic - equation of a line

Q: Find parametric equation of the line passing through point (4,2) and parallel to vector 7 = -i+5j.

A: Given: A line passes through the point (4, 2). The line is parallel to the direction vector…

Q: 2. Find the symmetric and parametric equations of the line containing the point A(1,2, 1) and x-2…

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Q: Find the parametric equations of the line contains point P (2, -1, 2) and tangent to the vector v =…

A: Given problem:- Find the parametric equations of the line contains point P (2,-1, 2) and tangent to…

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 the parametric equation for the line through the point (2,-3,1) and parallel to the vector…

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

A: Given plane is, 7x+4y+4z=15 Since, the line is perpendicular to the plane then the normal vector…

Q: 2: (a) Find parametric equations for the line through the point (-6, 1,2) and the point of…

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

A: We need to find the vector equation of the line of intersection. In order to get it, we’ll need to…

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

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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…

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A: Given that The point on the line (2,3,-1) and perpendicular to the plane 8x+3y+3z=5 A vector…

Q: Determine the parametric equations of the plane containing the point (1, -5, 9) and the line [x, y,…

A: I am going to calculate the parametric equations of the plane containing point (1,-5,9) and the line…

Q: Find the parametric equation of the line that passes through the point (4, -5, 0) and is…

A: We have to find the parametric  equation 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 the parametric equations of the line containing the point (-2,1,2) and parallel to the vector…

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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: 3. Find the parametric equation of the line passing through the point (-1,0, 3) and in the direction…

A: Equation of the line passing through the point (-1,0,3) in the direction N(7,0,-2) is   ( x+1)/ 7 =…

Q: (a) Find a parametric equation and symmetric equation of the line that pases through the point (2,…

A:

Q: Give a vector parametric equation for the line through the point (−1,−1) that is perpendicular to…

A: Vector equation of line which passes through point r0 and perpendicular to line a+bt,c+dt is given…

Q: 3. Find the parametric equation of the line passing through the point (-1,0,3) and in the direction…

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Q: Find parametric equations for the line described below. The line through the point P(1, 1, -2)…

A: Use equation of parametric line and put value

Q: The planes 5x+ 2y + 2z = 5 and 3x + 5y = -22 are not parallel, so they must intersect along a line…

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Q: Q2 What are the parametric equations for the line through the point (6,-3,1) that is orthogonal to…

A: We have to find the equation of parametric line

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

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Q: 10. Determine the scalar equation of a plane that is perpendicular to the line: |1,2, 3| + t|-2,4,…

A: A normal of a plane perpendicular to the line will be parallel to the line. So the plane is:…

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