Problem 1. Let P be the plane in R3 with parametric equation and let span | | 21 , 10 (Note that ...
5. Let P be the unique plane in R3 containing the points (1,3,2), (1,-1,0), and (2,0,1). (a) Find w, 21, 22 € R3 so that P=w+Span(21, 22) (b) Find y € R3 and tER? so that P=H. (Hint: cross product!)
Let C be the parametric curve (1) Determine the point(s) of intersection of C with the xz plane. (2) Determine the parametric equation of the tangent line to C at (1,1.0) (3) Find the plane that carries the tangent line found above and the vector (4) Set up but not solve, a formula that will determine the length of C for 1StS2 Let C be the parametric curve (1) Determine the point(s) of intersection of C with the xz plane....
Question 1 2 pts Describe the span of {(1,0,0),(0,0,1)} in R3 The x-z plane R3 R2 The x-y plane Question 2 2 pts Describe the span of {(1,1,1),(-1,-1, -1), (2,2, 2)} in R3 A plane passing through the origin Aline passing through the origin R3 A plane not passing through the origin A line not passing through the origin Question 3 2 pts Let u and v be vectors in R™ Then U-v=v.u True False Question 4 2 pts Ifu.v...
2z = 0 and let L denote the line with parametric equations Let P denote the plane with equation y=-2t1 z t3 Answer in the form (a,b,c) Find the point of intersection of P and L: Find the angle of intersection of P and L: degrees Answer in degrees with an absolute error of less than 0.1°
Find vectors V1, ..., VKE R3 that span the plane in R3 with equation x-2y+32 = 0. How many do you need? Hint: Write down a parametrized solution for the equation.
Find the parametric equation of the line in R3 in the direction v-(2,1,3) and containing the point P (-1,3,4). Find the angle between the vectors P and U.
4. Let S be a plane in R3 passing through the origin, so that S is a two- dimensional subspace of R3. Say that a linear transformation T: R3 R3 is a reflection about Sif T(U) = v for any vector v in S and T(n) = -n whenever n is perpendicular to S. Let T be the linear transformation given by T(x) = Ar, 1 1 А -2 2 2 21 -2 2 3 T is a reflection about...
1. For each of the following statements, declare whether the statement is true or false, (a) A system of four linear equations in three unknowns cannot have a solution. (b) 3.x + 3y - 2z = 0 is the equation of a plane through the origin in R', with normal vector (3,3. -2) (c) It is possible to determine if two lines in R3 intersect by solving an appropriate system of linear equations. (a) Find the parametric equation of the...
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).
(1) Equation of a Plane Let P(1,1,-1), Q(1,2,0), R(-2,2,2). (la) Compute PQxPR. (1b) Find the equation of the plane through P, Q and R in the form ax+by+cz=d. (10) What is the angle formed by this plane and the xy-plane?