2. Find a vector equation and parametric equations for the line segment that joins P to...
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...
equation for the line segment that joins (2,0,0) to (6,2,-2) 3) Find a vector equation for the line segment that joins (2,0,0) to (6,2,-2) 3) Find a vector
2. (10 points) Starting with the vector parameterization, find the parametric equations of the line passing through the points P = (1,3, -2) and Q = (-2.0,3). = y =
Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q corresponds to t = 1.) P(0, 0, 0), Q(5, 8,5) r(t) = Represent the line segment from P to Q by a set of parametric equations. (Enter your answers as a comma-separated list of equations.)
(a) Give a set of parametric equations (with domain) for the line segment from (4, -1) to (5,6). (b) Give a set of parametric equations (with domain) for the ellipse centered at (0,0) passing through the points (4,0), (-4,0), (0,3), and (0, -3), traversed once counter-clockwise. (c) Find the (x, y) coordinates of the points where the curve, defined parametrically by I= 2 cost y = sin 2t 0<t<T, has a horizontal tangent.
1. Find a vector equation and parametric equations for a line passing through (-1,2,3) in the direction of Ŭ = i + 21 – R.
Let L be the line with parametric equations x=-5 y=-6- z=9-t Find the vector equation for a line that passes through the point P=(-3, 10, 10) and intersects L at a point that is distance 5 from the point Q=(-5, -6, 9). Note that there are two possible correct answers. Use the square root symbol 'V' where needed to give an exact value for your answer. 8 N
(1 pt) (A) Find the parametric equations for the line through the point P = (2, 3, 4) that is perpendicular to the plane 2x + 1 y + 3z 1 . Use 't', as your variable, t 0 should correspond to P, and the velocity vector of the line should be the same as the standard normal vector of the plane. X= y- (B) At what point Q does this line intersect the yz-plane?
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)
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