The plane passing through the 3 points A(4, -2, 1), B(4, -1,4) and C(1,-4,2) can be...
(41) find the equation of the plane passing through the points A(3,-2,0), B(2,0,3), and C(1,-1,1) in (i) vector form (ii) parametric form (iii) cartesian form
Problem 3 Consider the lines ti(t) = (1,0,–2)t + (1, -3, 2) and (t) = (0,1, -1)t + (2,0,1). (a) Find their direction vectors vị and v2. (b) Are the given lines parallel? Are they orthogonal? Explain your answers. (c) Find a parametric equation for the plane spanned by vị and V2. vers (d) Find a vector that is perpendicular to both vì and v2. (e) Find a Cartesian equation of the plane containing Vị and vŻ and passing through...
Question 4 6-69) Consider the following three points: a-0 b-3and c-1 a) Find the parametric vector equation of the plane which passes through these three [3 marks] b) Find the vector cartesian equation of the plane passing through the three points listed [2 marks] c) Hence, or otherwise, find the non-vector cartesian equation of the plane passing through 3 marks] points above. the points above. Question 4 6-69) Consider the following three points: a-0 b-3and c-1 a) Find the parametric...
Question 6: Score 0/1 Use the transformation U = y(x) - 2+4 to find the solution to the initial value problem (a) - 92)-+10 9(a)-071 y(4) = 4 (I) = Your response No answer Correct response x+2"(3 x-8)(1/2)-4 Grade: 0/1.0 Only enter precise Maple syntax as explained in the Guide to Online Maple TA Tests. In particular, remember that the basic arithmetic operations are +,- /and. Please note that you CANNOT omit 3x is not correct, 3x is. Total grade:...
(4 points) Let Are the vectors V1, V2 and V3 linearly independent? choose If the vectors are independent, enter zero in every answer blank since zeros are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. 1-1 Note: In order to get credit for this problem all answers must be correct.
1 point) Let H be the set of all points in the fourth quadrant in the plane V R2. That is, H- t(x, y) |z 2 0,y S 0. Is H a subspace of the vector space V? 1. Does H contain the zero vector of V? H contains the zero vector of V 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H,...
Q1. Q2. Q3. Q4. Question 4 (2 marks) Attempt 1 A surface is described by the equation re10y+9y For a surface defined by a vector R(t,y)y,z(ry), the element of surface area is given by dS For the given surface, determine the cross product Each component should be expressed using the correct Maple syntax; for example, one component might be: -31+7'x exp(-11 y) The first component of the cross product is The second component of the cross product is The third...
3. Determine plane equation passing through points A(3,1, -1), B(2, 3, 4), C(-2, -3,5) Show calculation steps clear and cleanly.
What is the signed magnitude c of the projection p correct choice above, find a number c such that po of z) onto z2)? More precisely, let u be the unit vector in the direction of the cu Express your answer in terms of a 1 for a1, a 2 for a2, and a 3 for as. (a 1+a 2V(a 3) a1+a What is the (vector) projection p) of z) onto ?Express your answer in terms of the signed magnitude...
1 4 3 13 The vectors V1 = | 2 and V2 = 5 span a subspace V of the indicated Euclidean space. Find a basis for the orthogonal complement vt of V. 8 36 4 13 Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. O A. A basis for the orthogonal complement vt is {}. (Use a comma to separate vectors as needed.) OB. There is no basis for the orthogonal...