(a) What is the slope of the line with vector equation r(t) =    −7 + 2t, 4 + 7t   ?(b) Find parametric equations of the line that passes through the point (1, −4) and is perpendicular to the line with vector equation r(t) = −7 + 2t, 4 + 7t . (Enter your answer as a comma-separated list of equations where x and y are in terms of the parameter t.)

Q: A) Find the parametric equations for the line through the point P = (3.-5, 1) that is perpendicular…

A:

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

A: Solved below

Q: Find parametric equations for the line through (- 1,6, - 1) perpendicular to the plane 7x+ 5y + 5z =…

A: to find the parametric equations for line passing through (-1, 6, -1) and perpendicular to 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: 3. Find a set of parametric equations for the line of the intersection of the planes 3x-3y-7z -4 and…

A:

Q: (A) Find the parametric equations for the line through the point P = (-5, 0, -3) that is…

A: Equation of line.

Q: Find the parametric equation of the line that passes through P(-2, 0, 3) and is parallel to the line…

A: Given that: Equation of line is:     x=-1+3t, y=2-2t, z=3+t  and the point is : P(-2, 0, 3)

Q: Find parametric equations of the line through (-3,0,9) that is parallel to 2i-6j+k. x(t)= 11 y(t) =…

A:

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

A:

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 parametric equations of the line through (-1, –1, 6) that is parallel to 2i – 4j+k. x(t) = y(t)…

A:

Q: Find parametric equations of the line through (-3,0, 4) that is parallel to 5i– 8j+k. x(t) y(t) =…

A: Parametric equations of a line passing through the point P(a,b,c) and parallel to the vector v→=…

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

A:

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

A: Parametric and vector equation of line

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: 1. Find both the vector equation and the parametric equations of the line through (−3​,5​,6​)and…

A:

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

A:

Q: Find the vector and parametric equations for the line through the point P(-2, 1, -5) and the point…

A:

Q: s) Find the parametric equations of the line that is perpendicular to the plane 2x +y+3z = 4 through…

A:

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…

Q: Find parametric equations, in terms of t, of the line passing through (2, 2, 12) and parallel to the…

A: Given: The line is passing through 2,2,12. Also, it is parallel to the line: x=5-9ty=2z=4+t The…

Q: Find parametric equations of the line through (–3, 0, 3) that is parallel to 5i – 8j+ k. x(t) y(t)…

A:

Q: 4. Find the parametric equation of the line through (1, 0, -2) and parallel to the line % (x – 4) =…

A: This is the answer of question no. 4.

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: Complete the parametric equations of the line through the point (4,-8,3) and perpendicular to the…

A: See this solution in below

Q: Find the parametric equations for the line through the point (1, 7, 2) that is parallel to the plane…

A:

Q: Find parametric equations for the line in which the planes x + 2y + z = 1 and x - y + 2z =-8…

A: x + 2y + z = 1 and x - y + 2z =-8 are the two planes.Let z=t So, the equations become:

Q: If x = 1- 2t and y = 1+t denotes the parametric equation of a line in 2D , then (-2,1) is a) A point…

A:

Q: Find parametric equations of the line through (-2, –1, 3) that is parallel to 2i – 3j+k. x(t) = %3D…

A:

Q: Find the symmetric and parametric equation of the line that is the intersection between the planes…

A:

Q: 9. (A) Find the parametric equations for the line through the point P = (-5, -1, -3) that is…

A:

Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y2 = 8 ,…

A: We have given the surfaces; And the point (2,2,8)

Q: Complete the parametric equations for the line where the planes -4x + 2y – 14z = – 32 and -x – y –…

A: Use parametric equation of tangent line

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

A: The direction vector for this line is v=2,-1,-5 and it must pass through the point -5,4,-1. Thus we…

Q: Give a set of parametric equations for the line L4 that lies tangent to the graph of the vector…

A:

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

A:

Q: A line has parametric equations x = 2 +3t, y = 1 + 2t, z = -6 - t, fort that belongsto the family of…

A: given parametric equation of line  is x=2+3ty=1+2tz=-6-t

Q: 47. Determine the vector and parametric equations for the line passing through the points P(-1,-3)…

A: We’ll answer the 47th question since we answer only one question at a time. Please submit a new…

Q: What is the parametric equations of the line through (2,2,2) parallel to the x- axis ? a) x = 2, y =…

A: 7) The Parametric equations of the line through (2, 2, 2)  parallel to x-axis is given…

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…

A:

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 parametric equations for the line tangent to curve of intersection of the surfaces x? + y² = 8 ,…

A:

Q: 3. Give the parametric and symmetric equations of the line that passes through the point (2,3,-1)…

A:

Q: Find the parametric equation of the line through (1, 0, -2) and parallel to the line % (x – 4) = ½…

A: according to our guideline we are supposed to answer only the first question if you want any…

Q: The line L is parallel to the plane x+y+z=2 and is perpendicular to the vector (-1,1,–2). If the…

A:

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.