Find the vector and parametric equations of the line through the points A = (2,4,7) and B = (−1,5,3).

Q: Develop vector and parametric equations for the line through (7,2,-1) and parallel to r = (4,7,0) +…

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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 described below. The line through the point P(-3, -4, -2)…

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Q: How would I solve this? Find an equation of the plane that passes through the given point and is…

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

A: Using the dot product equal to zero for perpendicular to the vectors.

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

A: we have to find

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

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Q: Give a vector parametric equation for the line through the point (3,4,−2) that is parallel to the…

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Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(-4, 8, 0),…

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Q: Find symmetric and parametric equations of the line through the two points (−3, 5, 2) and (1, −3,…

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Q: 10

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Q: Find the equation for the plane through the point Po = (7,2,3) and normal to the vector n= 4i + 6j +…

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Q: Determine vector and parametric equations for the line in R that passes through the points A(1,0, 1,…

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Q: Give the parametric and symmetric equations of the line that passes through the point (2,6, –1) and…

A: To find equation of line passing through the point 2,6,−1 and perpendicular to both vectors −4,3,−5…

Q: Find the equation of the plane through the point (-3,2, 0) and perpendicular to the vector (1,-2,5).

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

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

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Q: Find the symmetric equations of the line that passes through the point (3,6, –10) and is parallel to…

A: The line passes through a point means that the point lies on the line. The direction vector of 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 both the vector equation and the parametric equations of the line through (-3,3,7) and (3, -…

A: Consider the points <-3,3,7> and <3,-1,0>. The vector equation and the parametric…

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

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

A: Given:

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

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Q: Give the parametric equation of the line that passes through the point (−4, 3, −5) and is…

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

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Q: Find an equation of the plane passing through the point perpendicular to the given vector or line.…

A: Given point is (0,4,0) and normal vector is -7i+5j.

Q: Find parametric equations for the lines in The line through P(-2, 0, 3) and Q(3, 5, -2)

A: To find the parametric equation for PQ

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

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Q: Find the general form equation of the plane through the origin and perpendicular to the vector (4,…

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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: 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 general equation of the plane which goes through the point (3,1,0) and is perpendicular to…

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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 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: Provide the parametric and symmetric equations of the line that passes through the point (4, -3, 5)…

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

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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: Find the equation for the plane through the point Po = (2,7,6) and normal to the vector n= 3i + 5j +…

A: Given:-normal, n=3i+5j+6kpoint on the plane, P0=2, 7, 6let (x, y , z) on the plane vector (x-2)i+…

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 the equation of a plane that is perpendicular to the vector 2i+4j−3k and passing through the…

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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: Find parametric equations of the line passing through (3, −1, −3) and perpendicular to the line…

A: The required line is passing through the point 3,-1,-3 and is perpendicular to 3,-2,4 and 0,3,5.…

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

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Q: Find vector and parametric equations of the plane that contains the point P = (-3,1,0) and is…

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Q: Find the equation of the plane through the point (-3,2,0) and perpendicular to the vector (1, -2,5).…

A: Questions from vector calculus.

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 equation of a plane that is perpendicular to the vector 4i+4j−3k and passing through the…

A: On solving this we will get

Q: Find an equation of the plane that passes through the point P(-7,-2,5) and has the vector n = (-7,4,…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.