5. The vertices of a parallelogram are the origin and points A(-1, 4), B(3, 6), and...
Find the area of the parallelogram with vertices at A=(4,1, -1), B = (5, -6, -3), C = (-1, 2, –5), and D= (0, -5, -7). a) "V971 ob) 27/563 V 1595 od) " 3/59 e) <> 4V131
Find the area of the parallelogram with the following vertices: 11. (-2, 3), (5, 8), (3, 3), and (0, 8) 12. (-2, 7), (-4, 4), (-11, 4), and (-9, 7)
please answer both (12(8 pts) Find parametric equations of the line through the point (2, -1,3) and perpendicular to the line with parametric equations 1-t,y 4- 2t and 3+ t and perpendicular to the line with parametric equations 3+t,y 2-t and z 3+2t. (13)(8 pts) Find the unit tangent vector (T(t) for the vector function r(t) - costi+3t j+ 2sin 2t k at the point where t 0 (12(8 pts) Find parametric equations of the line through the point (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...
(1) (a) Find the equation of the line, Li, which passes through the points A : (4,y,z) = (0, -5, -3) and B : (x, y, z)=(3, 1,0). (b) Find the equation of the line, Ly, which passes through the points C:(x, y, z)=(-1, -3,2) and D: (x,y,z) = (4,3,6). (c) Show that L and Ly are not parallel lines. (d) Write the parametric equations for L, and L2, and then show that the lines Li and L2 do not...
7. (-/1 Points) DETAILS LARCALC11 11.R.037. Find sets of parametric equations and symmetric equations of the line that passes through the two points. (For the line, write the direction numbers as integers.) (7, 0,5), (10, 11, 9) (a) Find sets of parametric equations. (Enter your answer as a comma-separated list of equations in terms of x, y, z, and t.) (b) Find sets of symmetric equations. *57 - 11 3+5 0 - 7x + 3 = 11y = -5z +...
1. For the following equation, find the center, vertices, foci, transverse axis, and asymptotes, and sketch the graph: 2. Consider the set of parametric equations (a) Graph in the following window: TMIN--3.74, TMAX- 3.74, TSTEP = 0.02, XMIN =-10, XMAX = 10, YMIN =-7, YMAX = 7, Sketch the graph. (b) At, find (x, y) and dy/dx. Write the equations of the lines tangent to and normal to the graph at (c) Find the length of the curve from to...
Verify that the points are the vertices of a parallelogram, and then find its area. (1, 1, 1), (4, 2, 3), (2, 5, 6), (5, 6, 8) STEP 1: Compute the following two vectors. (4, 2, 3) - (1, 1, 1) = (5, 6, 8) - (2, 5, 6) = Are these two vectors equal? Yes No STEP 2: Compute the following two vectors. (2, 5, 6) - (1, 1, 1) = (5, 6, 8) - (4, 2, 3) =...
Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(8,-8,5), C(10, -5, -2), D(3, 4, -4)
Find the area of the parallelogram with vertices A(-3, 3), B(-1, If a = (2, -1, 4) and b = (7, 2, 1), find the following. a xb = b x a = Find the cross product a x b. a = i+ 2j - 4k, b = -i + 5k