For each of the objects described below, state whether it is parallel, orthogonal or neither to...
Question 1 10 pts 1) Write a full sentence to answer each question. a) What information do you need in order to find an equation for a plane? b) Is 3x – 2y + 4z — 7 an equation for a plane? Explain. c) What information do you need in order to find parametric equations for a line? d) Are x = -1+ 3t, y= 2 + 4t, z= -3 + 7t, parametric equations for a line? Explain 2) Decide...
please answer question 4-7
Prove the arithmetic properties of the Cross Product 1. 2. a. Line L1 is parallel to the vector u Si+j, line L2 is parallel to the vector u-3i +4j and both lines pass through point P(-1,-2). Determine the parametric equations for line L1 and Lz b. Given line L:x(t)-2t+8,y(t)-10-3t. Does L and Ls has common 3. a. Find the equation of the plane A that pass through point P(3,-2,0) with b. Given A2 be the plane...
4. Find the parametric equations for a line through a point (0,1,2) that (a). parallel to the plane x + y + z = 2, and (b). perpendicular to the line T = 1+t, y = 1 –t, z = 2t (Answer: x = 3t, y=1-t, 2 = 2 - 2t)
Find the equation of the plane through the point (-2,8,10) and parallel to the line x=1+t, y=2t, z=4-3t
solve #5 with reasoning
5. (10 points) Find an equation for the plane in R3 that contains the line with parametric equations = 2t - 1, y = 3t + 4, and z = 7 - t and (2,5,0).
5. (a) Let u 1,4,2), ,1,0). Find the orthogonal projection of u on v (b) Letu ,1,0), u(0,1,1), (10,1). Find scalars c,,s such that 6. (a) Find the area of the triangle with vertices , (2,0,1), (3, 1,2). Find a vector orthogonal to the plane of the triangle. (b)) Find the distance between the point (1,5) and the line 2r -5y1 (i) Find the equation of the plane containing the points (1,2, 1), (2,1, 1), (1, 1,2). 7. (a) Let...
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i = (3,1,2) (b). Find the equation of a plane through Po = (2,3,1) and parallel to the plane P:3x + 2y -- z = 4 | Q4. Consider the line z-3 y-2 3 L, : * - - - L2: **** 2+5 y-3 -1 2 (i). Write the equations of both lines in parametric form (ii). Find the direction vectors V1, V2 of the lines...
I have attached the questions and the final solutions. Please do
all of questions 7 and 8
7. Given the line L:x,y,z-2,2,3+1,-1,-3, the plane S 3x-2y+2z-7 and the point A 1,1,1 a) Find parametric equations of the line which contains the point A, intersects the line and which is parallel to the plane b) Find parametric equations of the lne which contains the point A and which intersects the line Lat the&angle a) Show that V" is a subspace of...
Consider the following geometrical objects in R3: li: x=2 -21, y = -1, z = 2, ER 12: (x, y, z) = (0,5, -1) + (2, -1, 1), 1ER II : 3x + 4y - 2z = 1 II2 : 3x + 3y + z = -1 (a) Find the intersection point of , and 2. (b) Find the line 63 containing A(2,3,4) and is parallel to both II, and II. (c) () Determine whether II, and 2 are intersecting,...
At least one of the answers above is NOT correct. (1 point) Suppose f(x, t) = e 3t sin(x + 2t). (a) At any point (x, t), the differential is df = e^(-3t)cos(x+2t)dx+(e^(-3t))(2cos(x+2t)-2sin(x+2t))dt (b) At the point (-1,0), the differential is df = cos(-1)dx+(2cos(-1))+3sin(-1)dt (c) At the point (-1,0) with dx = -0.5 and dt = 0.3, the differential is df = 0.97344 Note. You can earn partial credit on this nrohlem (1 point) Consider the surface xyz = 20....