(a) Find a direction vector for the first line, which is given in parametric form. (b) Find parametric equations for the second line in terms of the parameter t. (c) Show that the two lines intersect at a single point by finding the values of s and t that result in the same point. Then find the point of intersection.

Q: -38, find parametric equations for the given curve. 3x 34. Segment joining (-3,0) and (0, 4)

A:

Q: c) Find the parametric equations of the line through the point (1,3,-2) and parallel to the vector V…

A:

Q: Sketch the curve represented by the parametric equation and indicate the orientation of the curve.…

A:

Q: 11. Find parametric equations for the line that contains the points P(2, -4, 7) and Q(0, –3, 5).

A: If Px0 ,y0,z0 and Qx1,y1,z1 are any two points then the parametric equation of the line containing…

Q: Example 1. Find parametric equations for the line through (-2,0,4) parallel v = 2i + 4j – 2k.

A:

Q: Find a set of parametric equations for the rectangular equation that satisfies the given condition.…

A: Given :                y = 2 x - 5  ,  t = 0        at point (3,1)

Q: Find the vector parametric equations of the two straight lines tangent to the given space curve

A: Given,              rt=2t2+3i+15t-7j+4t2+5kand  passing through the point P-3, -22, -7.

Q: Find a parametric equation of the line tangent to 7 (t) at the point (– 12, 144, – 4.159)

A:

Q: 2. Find the parametric equations of the line passing through the point (-1,4, –3) and is parallel to…

A: Given information is as below: r0=(-1,4-3)v=5i-j=(5,-1,0)

Q: 33. Find parametric equations for the path of a particle that moves along the circle x² + (y – 1)² =…

A: from the equation of a circle given to us, we have the radius r = 2 as the general form of the…

Q: 3. Find a set of parametric equations for the line of the intersection of the planes 3x-3y-7z -4 and…

A:

Q: he rectangular equation from the parametric equations by eliminating the paramet

A: 11. Obtain the rectangular equation from the parametric equations by eliminating the parameter t X=t…

Q: (3) Find a parametric equation for the line segment joining (1, 0, 1) and (0, –2, 1).

A: The direction vector of the segment is: (0,-2,1) - (1,0,1) = (-1, -2, 0) Initial point is (1,0,1).…

Q: Find parametric equations for the line that passes through the points P and Q. P(1, –2, 3), Q(5, 1,…

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

A:

Q: Sketch the parametric curve of the given parametric equations and indicate the orientation. 1. x=3t…

A:

Q: 117 Sketch the curve for each pair of parametric equations. 4t 2) x= -2t + 2, y = 1) x= 1, y=

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

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: • Sketch the curve represented by the parametric equations (indicate the Orientation of the curve),…

A: Given,

Q: 4. The trajectory of the spaceship Excelsior during the first 5 minutes of the launch can be…

A:

Q: 2. Find the parametric equations of the line passing through the point (-1,4, -3) and is parallel to…

A:

Q: Find the parametric equation for the line in R' that passes through the point (1, –2, 3) and that is…

A:

Q: Give a vector parametric equation for the line that passes through the point (3, 5, –5), parallel to…

A:

Q: Find a set of parametric equations of the line with the given characteristics. The line passes…

A: Let us assume that the given line is line1 to which our line AB is parallel. The equation of line1…

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: 5. Graph and find the parametric equations for the line through the point (1, -2, 3) and parallel to…

A: This question is about application line in 3d

Q: (a) Find parametric equations for the line that passes through the point (−4, 7) and is parallel to…

A: The line passes through the point (-4,7) and direction vector= &lt;6,-9&gt; [Because parallel…

Q: ANSWOT. 14. x 1+ y=t-1

A:

Q: Saved Match the parametric equation with the corresponding plane curve displayed. x-8-2 y-644 130…

A: Ttt

Q: 5. Find the parametric equations of a line through (1, 0, -1) and parallel to the line -(x-4) 1 y =…

A: Consider the given equation of the line. Converting it into the standard form and taking the…

Q: A ladder 25 feet long is leaning against the wall of a building. Initially, the foot of the ladder…

A: for the right angle triangle, use the Pythagorean theorem  ................(1) the location of the…

Q: (a) Find parametric equations for the line that passes through the point  (−3, 8) and is parallel to…

A: GivenLine passing through (-3,8)And a vector

Q: Q.1 Find the parametric equation of the line that 2)Passes point (1,3,7) and orthogonal to xy-…

A:

Q: find a parametric equation for the line that is perpendicular to the graph of the given equation at…

A:

Q: 2. Find the parametric equations of the line passing through the point (-1,4, -3) and is parallel to…

A:

Q: QV Find the Parametric equation for through a Point (5,3,-4) and Per Pendicudar to (ine Passes the…

A:

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

A:

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: A line passes through the point (- 8, – 9,9), and is parallel to the vector 9i + 6j + 7k. Find the…

A:

Q: 6) Find parametric equations for the line through P(0, -2,-2) and Q(1,1,0).

A:

Q: Find a set of parametric equations for the curve of intersection of a paraboloid x² + (y − 2)² = z…

A:

Q: (a) Find the parametric equations for the line segment that joins P(1, 0, 1) to Q(2, 3, 1).

A: Given, P(1,01), Q(2,3,1)

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

A:

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

A:

Q: 5. Find parametric equations for the line of intersection of the planes x + y = 1 and y +z = 1.

A:

Q: (3) Find parametric equations for the line of intersection of the planes. x + y - z = 2 and y + z =…

A: Given equation of the planes are  x+y-z=2     y+z=0 we rewrite them as x+y-z-2=0, and    0x+y+z=0…

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

A:

Q: 3. Find the Parametric Equations for the Curve. The line passing through (2, 6) and (3, 9).

A: Given, A line passing passing through the points 2, 6  and 3, 9 We have to write the parametric…

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.