9. (a) What are the two properties that determine a line in space? Give parametric equations for a line in space. (b) Find parametric equations for the line through the point (-2, 4, 1) and parallel to the vector v = (7, 5, 3).

Q: Find three different pairs of parametric equations for the line segmentthat starts at (0, 0) and…

A: Direction ratio is = (6-0, 6-0)= (6,6) That is equivalent to (1,1) , (2,2) and (3,3)

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…

Q: Find parametric equations for the line described below. The line through the point P(-1, -1, 5)…

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

Q: Find parametric equations for the line going through (5, 4, 6) and is perpendicular to the plane x −…

A: Here, By substituting the values of r0 and v in vector equation,

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 parametric equations for the lines in The line through (2, 4, 5) perpendicular to the plane 3x…

A:

Q: Can someone help me out with this question?

A: On a horizontal line, the y value is fixed.  And x values are changing.

Q: Find parametric equations for the line pass- ing through the point P(2, –1, 4) and parallel to the…

A: Given, The line is passing through the point  P 2, -1, 4  and parallel to the vector 1, 4, -2. We…

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…

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

A:

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

A: Given that z=x2+y2 and 3x−5y+7z=24 and point is 3,4,5. Let fx,y,z=x2+y2−z and gx,y,z=3x−5y+7z−24 We…

Q: 5. Find the parametric equations of the line that passes through the point (0, 1, 4)and is…

A: Given two vectors, u=2, -5, 1v=-3, 1, 4 Also, given the point, P=0,1,4 The cross product of u and v…

Q: 3. Does the parametric equation r = (2,-5,2) + s(1,4,2)+(-2,-3,1), s,/€ R, and the vector equation…

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Q: Determine vector and parametric equations for the line through the point (2, 1) and parallel to the…

A:

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: Find the parametric equation of the line through the points (−3, −2, 1) and(−1, −3, −1)

A: Given:

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

A: We have to find the parametric and symmetric form of the line perpendicular to the given plane at a…

Q: Find a set of parametric equations for the line passing through the point (7, o, 9) that is parallel…

A: Parametric equation of line in 3D

Q: (1 point) The planes 4x + 4y- z= 10 and 5x + 4y-4z 9 are not parallel, so they must intersect along…

A: The  intersection of two planes is always a line .

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

A:

Q: Determine parametric equations of the line of intersection of the planes x+2y+3z=4 and -2x+z=0. Then…

A: Let us consider two planes ax+by+cz+d=0 and a'x+b'y+c'z+d'=0  Intersection of two planes is line…

Q: find parametric equations for the lines with the given description.  Passes through (1, −1, 0) and…

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Q: Find a parametric representation of a straight line through (1,1,1) and (4,0,2), and sketch it using…

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Q: 3. Give the parametric and symmetric equations of the line that passes through he point (4, –3, 5)…

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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: find parametric equations for the lines with the given description.  Perpendicular to the yz-plane,…

A: To find parametric equation perpendicular to yz plane passes through (0,0,2)

Q: 3) Find a vector equation and parametric equations for the line segment that joins (-2, 4, 0) to…

A:

Q: 1) Find parametric equations for the line of intersection of the planes 2л + 5у — 32 — 10 and х —…

A: The parametrc equation of a line with direction vectorabcand passing through a point x0,y0,z0 are…

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

A: We have to find the equation of the line passing through the point (1,2,-1) and normal to the plane…

Q: Find parametric equations of the line containing the .point (2, 3,-1) and normal to the plane x+…

A:

Q: Give a vector parametric equation for the line through the point (4,-3) that is perpendicular to the…

A: Give a vector parametric equation for the line through the point (4,-3) that is perpendicular to the…

Q: Find the parametric equations for the line through the point P=(-5,4,-1) that is perpendicular to…

A: The equation of the plane is given by 2x-y-5z=0. The directional cosine of the normal to this plane…

Q: Find the parametric equations of the line containing the point (-2,1,2) and parallel to the vector…

A:

Q: Find parametric (or vector) and symmetric equations of the line which pass through the points P,…

A: P11, 4, 6 & P22, -1, 3. Vector equation of a line passing through two points with position…

Q: 1. Find the vector and parametric equations for a line passing through (7,-4, 2) and parallel to the…

A: We have to find the vector and parametric equation of the line

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: Find parametric equations for the line described below. The line through the point P(2, 3, 3)…

A: To find the parameter equation of the line passing through point P(2, 3, 3) parallel to the vector…

Q: Find the parametric equations for the line through the point P = (-1, 4, -4) that is perpendicular…

A: Normal vector perpendicular to the plane 2x−4y−2z=1 is: (2, -4, -2) The line passes through P = (-1,…

Q: Find the parametric equation for line l that is parallel to line m with equation: x = 1 + 4t; y = -…

A: Two lines are said to be parallel if their direction ratios are proportional. We will use this fact…

Q: Give a vector parametric equation for the line through the point (4, 0, -5) that is parallel to the…

A:

Q: Write the parametric equations of the line through the point P (-6, 4, 3), that is perpendicular to…

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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:

Q: A line with parametric equations r = 10 + 2s, y = 5 + 5,2 = 2, sER, intersects a sphere with the…

A:

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: Find the parametric equations of the line that is perpendicular to the plane 2x +y +3z = 4 and goes…

A:

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

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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