Problem 2. (1 point) Find a unit vector with positive first coordinate that is orthogonal to...
(a) Find a unit vector that is orthogonal to the plane through the points P(0,0,–3), Q(4,2,0), and R(3,3,1) (b) Find two non-parallel vectors that are orthogonal to the vector Ŭ = i + 2) + 3k (c) Find the angel between the vector Ở = 51 + 21 – k and the z - axis (d) Describe why it is impossible for a vector to have the following direction angles 511 6 -, B = 3, and y TT π...
Chain Rule Tangent Planes: Problem 10 Previous Problem Problem List Next Problem (1 point) Consider the surface xyz = 6. A Find the unit normal vector to the surface at the point (1,2,3) with positive first coordinate. 0 B. Find the equation of the tangent plane to the surface at the given point Express your answer in the form ar+by+c+d normalized so that a 6. Note: You can earn partial credit on this problem Submit Answers Preview My Answers You...
Previous Problem Problem List Next Problem (1 point) Find the derivative of the vector function r(t) = ta x (b + tc), where a = (2, -4,-2), b = (3,1,5), and c = (2,1, -2). r'(t) =( Note: You can earn partial credit on this problem Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Email WebWork TA
Problem-1 (10 points): The line L through the point p(-1,0,1) is orthogonal to the surface S-((r, y.3)r In:+sin(y:)- 0 at p. Then L intersects the plane :-0 at the point Problem-1 (10 points): The line L through the point p(-1,0,1) is orthogonal to the surface S-((r, y.3)r In:+sin(y:)- 0 at p. Then L intersects the plane :-0 at the point
1. (1 point) Find two vectors vi and v2 whose sum is (-3,0), where Vi is parallel to(-2,-4) while v2 is perpendicular to-2,-4) and Answer(s) submitted: (incorrect) 2. (1 point) Find the angle θ between the vectors a- 10i -j- 5k and b 2i+j- 21k Answer (in radians): θ Answer(s) submitted: (incorrect) 3. (1 point) Find a vector a that has the same direction as -6,5,6) but has length 3. Answer: a Answer(s) submitted: (incorrect) 4. (1 point) Suppose we...
Thanks so much! 14. Find the vector form and the point normal form of the equations for the plane through the three points P = (3,3,3), Q = (1, 2, 2),and R = (1,5,1). Note that these points are not vectors. Show the calculation of the normal vector. Don't forget to give both forms and show your calculations. [8 points)
Assignment 9: Problem 3 Previous Problem List Next (1 point) The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but no top.) The side of S is given by x2 +y2 = 9, and its height is 2. (a) Give a parametric equation, rt) for the rim, C r)= with (For this problem, enter your vector equation with angle-bracket notation: < f(t), g(t), h(t) >.) (b) If S is oriented outward and...
Consider the points below. P(1, 0, 1), ((-2, 1, 3), R(4, 2, 5) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (b) Find the area of the triangle PQR.
(1 point) (a) Find a unit vector from the point (2, 1) and toward the point Q = (10, 16). P= už (b) Find a vector of length 51 pointing in the same direction. v=
Problem 2. Find a vector 7 orthogonal to the row space, and a vector y orthogonal to the column space of the matrix [1 2 1] 2 4 3 [36 4