3. Find a parametric equation of the line that contains the points (1, 1) and (-2,...
The parametric equations where 0 tl describe the line segment that joins the points P1(x1, y and P2(x2, y2) Use a graphing device to draw the triangle with vertices A(1, 1), B(3, 4), C(1,7). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma- separated list of equations. Let x and y be in terms of t.) A to B B to C A to C
The parametric equations where 0 tl describe the line...
4. (10 points) (a) Find a parametric equation and symmetric equation of the line that pases through the point (2, -1, 3) and is parallel to the vector 7 +27 -37. (b) At what points does this line intersect the yz-plane?
Find a vector parametric equation F(t) for the line through the points P= (1,1, 4) and Q = (-2,-2,8) for each of the given conditions on the parameter t. (a) If 7(0) = (1,1, 4) and 7(5) = (-2,-2,8), then F(t) = HI (b) lf F(7) = P and 7(11) = Q, then F(t) = HI -2, respectively, then (C) If the points P and Q correspond to the parameter values t = 0 and t F(t) =
Give parametric equations that describe a full circle of radius
R, centered at the origin with clockwise orientation, where the
parameter t varies over the interval [0,22]. Assume that the
circle starts at the point (R,0) along the x-axis.
Consider the following parametric equations, x=−t+7, y=−3t−3;
minus−5less than or equals≤tless than or equals≤5. Complete parts
(a) through (d) below.
Consider the following parametric equation.
a.Eliminate the parameter to obtain an equation in x and y.
b.Describe the curve and indicate...
The parametric equations below describe the line segment that joins the points P1(X1,Y1) and P2(x2,12). Consider the triangle A(1, 1), B(4,2), C(1, 4). Find the parametrization, including endpoints and sketch to check. X = X1 + (x2 - X1) y = V1 + (Y2 - Y1)t Ostsi (a) A to B x(t) = 1 + (2-1) y(t) = 1+(3-1) ostsi (b) B to C x(t) = (t) = Ostsi (c) A to C X(t) = y(t) = Ostsi
Find parametric equations for the line described below. 30) The line through the points P(-1, -1, -1) and Q(7,-5,7) Find a parametrization for the line segment beginning at P1 and er 31) P1(3, 0, -2) and P2(0, 5, 0)
[G] Find the parametric equations for the curves described below. Then write the corresponding vector-valued function that represents the given curve. Be sure to include an appropriate interval for the parameter. *Make sure you give both the parametric equations and vector- valued function and don't forget the interval for the parameter either. (G.1) The line segment from (-3,4,7) to (6,4,0). (G.2) The segment of the curve with equation y = (x + 4 from (12,4) to (-3,1). (G.3) The lower...
5. (20 points) Given a line segment L1, defined by the parametric equation to follow, find another line segment with length 3 which is perpendicular to L1. Note: more than one solution exists.
1:34 Find the parametric equations of the line in Rthat passes through the points (2,4, 1) and (-3, -2,-4). (A) x 25t y 6 6 (B) x 2-5t y 4 6t (C) x -3-5t y 4 6t (D) х--2-t y 6-6t y 6-6t (G) x 2 -5t y 4 6 Problem 45
Find a vector equation and parametric equations for the line segment that joins P to Q. (D |-1+2-) 1 P(0, -1, 4) 4 -t.2 3 t. r(t) 4 vector equation X 7 4 t.2 3 1 - t. (x(t), y(t), z(t)) 4 X - parametric equations 2 If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might...