Find sets of (a) parametric equations and (b) symmetric equations of the line that passes through the point (−3, 0, 2) and is parallel to the vector or line      v = 6j + 3k. (For each line, write the direction numbers as integers.)

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…

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

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Q: Find sets of (a) parametric equations and (b) symmetric equations of the line that passes through…

A: The direction ratio of the given line x = 3 + 3t, y = 5 − 2t, z = −7 + t is  (3,-2,1).   Given that…

Q: find parametric and symmetric equations for the line through (1,-1,2) and parallel to the line…

A: From the line x+2=y-1=z  we get the direction ratio=(1,1,1)The direction ratio of the parallel line…

Q: Find the parametric equation of the lines passing through (4, -2, 5) and (-3, 0, 6)?

A: Consider the two given points (4,-2,5) and (-3,0,6). The objective of the problem is to find the…

Q: Write the equation of the line passing through P with direction vector d in vector form and…

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Q: Give the equation of the line in vector form, parametric form and symmetric form. The line through…

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Q: c-) Represent in a Cartesian system the graph of these two lines. d-) Give a vector equation for…

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Q: Find parametric equations for the lines in The line through the origin parallel to the vector 2j + k

A: Given  The vector equation is  0i +2j+k  The line passing through origin , origin is  ( 0 ,0 ,0)…

Q: 2. Find an equation of the plane parallel to the line

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Q: Describe all solutions of A X = b, where 2 -5 31 A = |-2 6 -5 and b = |-4 7 0 2 Describe the general…

A: The given matrix are: A=2-53-26-5-470B=-4214 The Augmented Matrix is given by:…

Q: Complete the parametric equations of the line through the point (-2,-4,-8) and perpendicular to the…

A: Given: Equation of plane x-3y-5z=2 Point (-2,-4,-8)

Q: Give the equation of the line in vector form, parametric form and symmet The line through the point…

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Q: Find the parametric equations of the line through the point P(1, 2, 4) and parallel to the vector .

A: use the parametric form  of line .

Q: Find the vector, parametric, and symmetric equa lines: (a) the line perpendicular to x+7_y-4 with 3…

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Q: Find sets of (a) parametric equations and (b) symmetric equations of the line that passes through…

A: We have to find sets of parametric equation and symmetric equations of line that passes through the…

Q: Given the same three points P (1, 4, 6), Q (-2, 5, -1)  and R (1,  -1, 1). Find a vector equation,…

A: Solve the following

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

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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 an equation for the set of all points equidistant from the point (0, 0, 2) and the xy-plane.

A: Let any such point is given by (x,y,z)(x,y,z) is z units away from the xy plane.

Q: 4. (a) Find a parametric equation and symmetric equation of the line that pases through the point…

A: We have a point P(2,-1,3) and a vector  i^+2j^-3k^ We have to find a parametric equation and…

Q: Find the vector parametric equations for the line. in the direction of the vector 57-5-k and through…

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Q: Determine the vector and parametric equations of the line through A(6,2,5) and B(9,2,8)

A: Given points , A(6,2,5) B(9,2,8) Therefore a=6i+2j+5k b=9i+2j+8k

Q: Find a parametric equation and symmetric equation of the line that pases through the point (2, -1,3)…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: The symmetric equations for the line passing through (-3,–4, -5) and parallel to the vector (1,7,–…

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Q: A volleyball is hit when it is 4 ft above the groundand 12 ft from a 6-ft-high net. It leaves the…

A: Given information: A volleyball is hit when it is 4 ft above the ground and 12 ft from a 6-ft-high…

Q: Find parametric equations for the lines in The line through (2, 3, 0) perpendicular to the vectors u…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Write vector and parametric equations of the line. a) parallel to the line x+6y = 1 and through the…

A: We know that the line equation of the line that passes through point (ro→), and parallel to vector…

Q: Find the equation of a plane through the point (3, -2, 8) and parallel to the plane z=x+ y.

A: Given, Plane is passing through the point (3, -2, 8) and Parallel to the plane z=x+y    Equation of…

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 parametric equations for the line in which the planes 3x - 6y -2z = 15 and 2x + y - 2z = 5…

A: Equation of plane - 1,3x-6y-2z = 15 Normal vector of plane 1 = n1 = 3,-6,-2…

Q: 4- Find parametric and symmetric equations of the line passing through the points (1,- 1,2) and…

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Q: Find the parametric and symmetric equations for a line that passed through the points (2,0,8) and…

A: Representing the points as the points vectors we get,  2,0,8 and -2,6,4 The direction numbers are…

Q: Find a vector equation of the line that passes through A(5,-4) and B(1,-1)

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Determine the parametric and symmetric equations for the line through the given points (2, –7,5),…

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Q: write the equation of the line passing through P with direction vector d in (a) vector form and (b)…

A: Given the point P=(-4,4) and the direction vector d=11We need to find the equation of line passing…

Q: Find parametric equations for the lines in The line through the point (3, -2, 1) parallel to the…

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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: Give a vector parametric equation for the line through the point (-2, –2) 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…

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Q: give the equation of the line in vector form, parametric form and symmetric form. 11) The line…

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Q: write the equation of the line passing through P with direction vector d in (a) vector form and (b)…

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Q: Give the parametric and symmetric equations of the line that passes through the point (5,−1,3) and…

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Q: omplete the parametric equations of the line through the point (-3,2,4) and parallel to the vector -…

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