24) Consider line L of parametric equations x =t, y = 2t, z = 3, t E R. a. Find parametric equations for a line parallel to L that passes through the origin. b. Find parametric equations of a line skew to L that passes through the origin. c. Find symmetric equations of a line that intersects L and passes through the origin.

Q: The set of parametric equations represents a line. Without eliminating the parameter, find the slope…

A: Using chain rule.

Q: 1) Find the parametric equations of the line that is tangent to circle x² + y2 = 25 %3D at point (3,…

A: Given: Equation of circle: x2+y2=25 and tangent at point 3, -4

Q: find parametric equations for the given curve.  Line through (2, 5) perpendicular to y = 3x

A: Find parametric equations for the given curve.  Line through (2, 5) perpendicular to y = 3x

Q: The parametric equation of the line resulted from intersection of x-y 0, and z = 2 is %3D

A: Use the given planes.

Q: Suppose a curve is given by the parametric equations x = f (t), y = g (t), where the range of f is…

A:

Q: Suppose parametric equations for the line segment between (-2, 8) and (7,3) have the form: a + bt…

A: This question can be solved by substituting the values of x,y and t in the given equations.

Q: Find parametric equations for the line segment joining the points (5, 3) and (11, 11). x=t, y = 3 +…

A: Solution

Q: Describe the relationship between the lines with the following parametric equations: x = 1- 41, y =…

A:

Q: (d) Find the parametric equation for the line segment from point P(1,3, 2) and Q(1, –1,6).

A:

Q: Eliminate the parameter to write the parametric equations as a Cartesian equation. If x(t) = 3t – 2,…

A:

Q: Let / be the line given in parametric form by the equations x = 1 + 21 y = -1 + 31 z = 2 + 51 What…

A:

Q: Find the distance between the point (1, −2, 4) and the line given by the set of parametric equations…

A: The given point is M=(1, −2, 4) The direction vector of the line is =s=(2,1,2) A point on the line…

Q: Consider the curve C given in parametric equations as

A: In this question, we find the tangent line and normal line along with that we find the point where…

Q: Consider two straight lines described by the following parametric equations x = 3+t, y = 4 + 3t, z =…

A: The angle between two vectors  v1 and v2  is,…

Q: Cannot solve

A:

Q: In Exercises 23–38, find parametric equations for the given curve. 30 31. Line through (3, 1) and…

A: Consider the points of line, (3, 1) and (-5, 4) To calculate the equation of line passing through…

Q: Find parametric equations for the line through P = (2, 5) perpendicular to the line y = 4x − 3.

A: Given line, y = 4x − 3. To find the parametric equations for the line through (2,5) and…

Q: Suppose parametric equations for the line segment between (2, a(t) 6) and (0, 0) have the form: = a…

A: Explanation of the solution is given below...

Q: x = 12 + 3 y = 2t [-2, 2]

A: Substitute t value

Q: Suppose parametric equations for the line segment between (0, - 6) and (9, – 8) have the form: (t) —…

A: Suppose parametric equations for the line segment between 0,-6 and 9,-8have the form xt=a+bt…

Q: Find parametric equations for the path of a particle that moves along the circle æ² + (y – 1)² = 4…

A: As per our guidelines we are supposed to solve only one question. For the first question follow the…

Q: Suppose parametric equations for the line segment between (5, – 8) and (3, – 1) have the form: s#(t)…

A:

Q: ) Find parametric equations for the line segment starting at P(-1,-3) and ending at Q(6,-16).

A:

Q: ) (i) Find the parametric equations for a smooth curve, C: x= 4z, y = -3z that joins two points,…

A:

Q: A curve represented by the parametric equations a = et and y = e 24, will be Select one: О нурerbola…

A:

Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 3x + 4y +…

A:

Q: Question 2. (a) Prove that the lines with parametric equations: x = 1+t, y =1+ 6t, z = 2t and x = 1+…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Find the parametric equations for the path of a particle that travels three quarters of the way…

A:

Q: Try to sketch by hand the curve of intersection of the circu- lar cylinder x + y² = 4 and the…

A: Given, Circular cylinder, x2+y2=4 Parabolic cylinder, z=x2

Q: Consider the point (−6, 2, 2), line l : (1 − x)/7 = y − 3 = z/2. Find parametric equations of the…

A:

Q: Find parametric equations for the line segment joining the points (-6, 4) and (2, 3). x=-6 + 8t, y =…

A: Parametric equation of line segment.

Q: Find the distance between the point (2, 3, 2) and the line given by the set of parametric equations…

A:

Q: Find the parametric equations for the line through the point (5, 2,9) and perpendicular to the plan…

A:

Q: Suppose parametric equations for the line segment between (2,4) and (−2,2) have the form: x(t)=a+bt…

A:

Q: Given two points P(6, 3,1) and Q (5,0, 0), find the parametric equations for a smooth curve, C:x= 5+…

A:

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A:

Q: Let Lj and L2 be the lines whose parametric equations are Li :x = -10+21, y = 25 – 81, z = 17 – 6t…

A: L1 : x=-10+2t,  y=25-8t,  z=17-6tL2 : x=52-6t,  y=-43+4t,  z=20-3t

Q: Find the parametric equations for the line passing through points P(2, -3, 1) and Q(4, 1, -4)

A: Given points are  P2,-3,1,Q4,1,-4

Q: What are the direction numbers of a line given by the parametric equation:  x=6+t,y=5+4t,z=1−2t

A:

Q: The curve above is defined by which of the following sets of parametric equations?

A:

Q: Verify algabraically whether the parametric equation x(t) = 10-2.5t, y(t) = 1.5t and the rectangular…

A:

Q: Find two different sets of parametric equations for the rectangular equation  y = 4x + 1, t = −1 at…

A: Given equation is y=4x+1, t=-1 and the point is (-2,-7).

Q: find parametric equations for the given curve. Segment joining (1, 1) and (2, 3)

A:

Q: Find parametric equations for the line through (8,4,6) parallel to the x-axis. X = y = - o <t< ∞

A: The equation passing through point (8,4,6). The parametric equation passing through point (8,4,6)…

Q: Find the distance between the point (4, −1, 5) and the line given by the set of parametric equations…

A: The point is: P(4, −1, 5) The line is: x = 3, y = 1 + 3t, z = 1 + t The line is: &lt;3, 1, 1&gt; +…

Q: Find a set of parametric equations for the rectangular equation that s y = 2x – 3, t = 0 at the…

A: let x = t + a put all the given points to find out the value if a x = 4 and t = 0 4 = 0 + a a = 4 so…