(a) Write the vector or parametric equations of the line through the point (2,0, 3) and perpendicular to the vector (1, -5, 1). (b) Determine if the two lines are perpendicular, parallel or neither: r(t) = (t, 9 - t, 1 + 3t) and p(s) = (2 + 8s, -8s, 6 + 24s)

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A: Given points are: A=3,1,-1 and B=7,0,1 To find the vector, parametric, and symmetric equations

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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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A:

Q: If a line is parallel to the vector 8i + 5j + 3k and passes through the point P = (6,2,4), then the…

A:

Q: 6. Find the vector, parametric and scalar equations of the plane that contains the points A(-1,2,5)…

A: The points are A(-1, 2, 5) B(3, 2, 4) and C(-2, -3, 6) AB→=324--125=20-1AC→=-2-36--125=-3-51 The…

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A:

Q: 1.Find the vector equation and parametric equations of the line passing through the point P(5, 6, 7)…

A:

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 the vector and parametric equations for the line through the point P(-5, -3, -4) and the point…

A: Given: P(-5,-3,-4) and Q(-2,2,-5) To find the vector r(t) and the parametric equations for x(t),…

Q: 1. Determine vector and parametric equations of the plane that contains the points A(1, 2, -1), B(2,…

A: Since you have posted multiple questions. we will solve first question only due to the bartleby…

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

A:

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

A:

Q: (a) Determine the vector and parametric equations of the line containing points E (-1, 5) and F (6,…

A:

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: 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 the vector equation and parametric equations of the line passing through the point P(5, 6, 7)…

A: Given problem :

Q: If a line is parallel to the vector 4i + 10j + 7k and passes through the point P = (7,7,4), then the…

A: Solution

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

A:

Q: Which of the following is a direction vector for the plane with Cartesian equation 3x -2y - 5z + 3 =…

A: To find a direction vector for the given plane. The general form of plane with cartesian equation…

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

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Q: 5) Write the equation of the line through the points P(1,3,7) and Q(2,5,11) in: a) Vector form b)…

A: topic - equation of line through two points

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: Find parametric equations for the line through the points P(-1,-1, 7) and Q(3, -4, -1) O x = 4t - 1,…

A:

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

A:

Q: Find Vector, Parametric and Scalar equations for the line that passes through t -2,11) and (6,1).

A: Given: - The line that passes through the points -2,11and 6,1. To find: - The parametric equations…

Q: 3. Find an equation of the plane passing through the points (1, 2, -6), (2, 3, -2), and (-1, 4, 8).…

A:

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…

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A:

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

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A: Equation of line passing through the point (x1,y1,z1) and is perpendicular to the plane (ai+bj+ck)…

Q: If a line is parallel to the vector 6i + 7j+ 2k and passes through the point P= (5, 1,7), then the…

A: Given that a line is parallel to the vector 6i+7j+2k and passes through the point P=5, 1, 7. We know…

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: If a line is parallel to the vector 3i + 9j+ 6k and passes through the point P = (5, 5, 4), then the…

A:

Q: If a line is parallel to the vector 3i +2j+ 1k and passes through the point P = (1,3,8), then the…

A:

Q: Find parametric equations for the line through p (2,3,0) and perpen-dicular to the vectors u =(1,…

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

A:

Q: Find parametric equations for the lines in Exercises 1–4. 1. The line through the origin parallel to…

A: Hey, since there are multiple questions posted, we will answer the first two questions. If you want…

Q: Which of the following is the vector equation of a plane that contains the line x-3y+2 2-1 5 -23 and…

A: We know r→ = a→+s→+t→ From the equation of line, we get a→ = 3i^-2j^+k^ or we can write it as 3, -2,…

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

A: Consider the given parametric equation of line 5+4t,5t−3Find the parametric equation of the line…

Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4, 2)…

A:

Q: 1. a. Show that two lines with direction vectors d, = (2,3) and d, = (6,-4) are perpendicular. %3!…

A:

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

A:

Q: If a line is parallel to the vector 7i +9j + 9k and passes through the point P = (10,4, 1), then the…

A:

Q: If a line is parallel to the vector 7i + 5j+ 5k and passes through the point P=(4,3,5), then the…

A: To find the parametric equation of the line:Given line is parallel to the vector 7i+5j+5kSo, a=7,…

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

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.