Find a vector parallel to the line defined by the parametric equations x(t) - 3 – 9t y(t) 2 + 7t z(t) 4 – 10t Additionally, find a point on the line. Parallel vector (in angle bracket notation): Point:

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

A: Find the vector and parametric equations for the linethrough the point P4,-2,4 and parallel to the…

Q: 33 and Complete the parametric equations for the line where the planes – 3x – 9y – 12z = - 11x + 2y…

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Q: Find a vector parametric equation r(t)|for the line through the points P = (-3, –2)|and Q = (-5,…

A: According to the problem, we have

Q: Find the symmetric and parametric equations of the line containing the origin and is perpendicular…

A: .

Q: 1. Find parametric equation for the line through the point P(3,-4,-1) parallel to the vector v…

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Q: Complete the parametric equations of the line through the point (-6,0,-8) and perpendicular to the…

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Q: Find the parametric equations for the lines. Where, the line through the point P (3, -4, -1)…

A: Topic = Vector

Q: 31. (a) Show that the parametric equations x = x, + (x2 – x1)t y = yı + (y2 – yı)t where 0 <t< 1,…

A: Given data: The first parametric equation is x=x1+(x2-x1)t. The second parametric equation is…

Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: a +…

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Q: 3+z Given the points R (1, -1, -3), the vector v = and the line d: ¯x+¹=1+y= 3 2 3. Calculate the…

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Q: Find the real number a such that the line of parametric equations x = t, y = 2 – t, z = 3 + t, te R…

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Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: x2 +…

A: Here we have to find the parametric equations of the curve C of intersection of the cylinder S:x2+y2…

Q: 19. Find y' in the parametric equations x =, t-1 t+1 A) (f – 1) 7-1 B) (1+ 1)? 2 +1 C) (1+1)? t +1…

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Q: (1 point) Given a the vector equation r(t) = (4 + 4t)i + (1 + 1t)j + (1 + 4t)k, rewrite this in…

A: See below the answer

Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x = 2 + 3t…

A:

Q: a) Find the scalar parametric equation and vector equation (r = c + ta) of the straight line z+5 x –…

A: We have to find

Q: The angle and the parametric equations for the intersect line between planes a + y = 1, and 2r+y-2z…

A: Given, x+y=1, 2x+y-2z=2 we know angle between two plane is…

Q: 3. What is the parametric equation for the line through the point (1 ,2, 3) parallel to the x- axis?…

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Q: L0. Find parametric equation of the line perpendicular to the lines 11: x = 1-1, y=t, z= 2t -1 and…

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Q: Find parametric equations for the line through the point, that is parallel to the given plane, and…

A: given point 0,2,2 given plane x+y+z=3 given line x=1+t,y=2-t,z=2t

Q: Line l is given by the parametric equations: x = 1-2t  y = -2+4t z = 4+5t Determine the equation…

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Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: x2 +…

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Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 2x + 4y +…

A: Equation of line normal to graph of functions f(x) is :  r&lt;t&gt; = &lt;x0,y0,z0&gt; +…

Q: Find the parametric equation for the line where the planes 4x – by + 8z = - 36 and – by + z = – 15…

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Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: æ? +…

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Q: Complete the parametric equations for the line where the planes - 7x + y + 3x = 3 and 4x7y + z = 23…

A: Given two planes -7x+y+3z=3 and 4x-7y+z=23

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

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Q: What is the parametric equation for the line through the point (1,2,3) parallel to the y- axis? (a)…

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Q: Q1: Two lines in space {x 1- 2t,y 2 +3t,z =-1+t} and {x = 1+t,y% 3+ 2t,z = -1+3t} find the angle…

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Q: 1/a- Find the parametric equation of the line passing through Po(1,3,4) parallel to 21-j+5k b- Find…

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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…

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Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (2, –5) + t(1,…

A: Parametric equation of the line, &lt;x,y,z&gt;=&lt;a,b,c&gt;+t&lt;p,q,r&gt; , t is a scalar is given…

Q: Find the parametric equations for the line of intersection of the planes x+y-z = -20 and 9.x + 3y +…

A: Given planes, x+y-z=-20 and 9x+3y+z=16. The objective is to find the parametric equations for the…

Q: 22. Find (a) parametric equations for the line of intersection, and (b) the cosine of the angle…

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Q: 3. What is the parametric equation for the line through the point (1,2,3) parallel to the y - axis?…

A: The solution is given as follows

Q: Complete the parametric equations of the line through the point (-3,1,-4) and perpendicular to the…

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Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve),…

A: Given parametric equations, x=et,y=e3t+4 To find y.

Q: Find the parametric equation for the line where the planes 4x – 6y + 8z = - 36 and – 6y + z = – 15…

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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: Find a vector equation for the line through the point P = (4, -2, -4) and parallel to the vector vv…

A: P= (4,-2,-4) is a point on the line.  And the line is parallel to v=(4,-1,4)  v is the velocity…

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

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Q: Q.1 Find the parametric equation of the line that 1) Let L1: x = 2t – 1, y = 3 +t,z = t – 1/2 Find…

A: Given parametric equation of line  x=2t-1 y= 3+t  z= t-1/2   As per our guidelines we are supposed…

Q: Q5) Find the angle between the plane x+y-z=3 and the plane that perpendicular to the line has the…

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Q: B Find the parametric equation of the plane passes through the point (-3,0,7) and perpendicular to…

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Q: Q. Find parametric equation of the line perpendicular to the lines l1: x = 1- 1, y=t, 12 : z = 2t –1…

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Q: The angle and the parametric equations for the intersect line between planes a+y = 1, and 2r +y - 2z…

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Q: Complete the parametric equations of the line through the point (8,6,-2) and perpendicular to the…

A: equation of line passing passing through the point 8,6,-2 and perpendicular to the plane , x-7y-z=-3

Q: Find the parametric equation of the line passing through P (1, 2, 3) and perpendicular to the lines…

A: Given:  r1= (2+t)i + (1+2t)kr2=(-t)i + (1-6t)j - (2t)k

Q: Find parametric equations for the line segment from  (9, 2, 1) to (5, 5, −1).  (Use the parameter…

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Q: Suppose F(x, y) = x?i+ y?j and C is the line segment segment from point P = (-5, –5) to Q = (-3,…

A: Given data: The given expression for the vector is F→(x,y)=x2i→+y2j→. The given first point is…

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.