Solution : ( 8 )
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8. A parallelepiped is formed by the vectors a,1,0, b 0,1, 1 and c1,1 e the...
Problem 3. (8 points) Given that the interpolation polynomial of the points (-3,2), (-2,1),(-1,-1), (0,1), (1,0), (2,0), (3, 1) is 191 13 5 781 , 53 Q(x) = -3602 + 30++ Find a polynomial curve passing through these seven points and additionally the point (4,0). Write your polynomial in standard form anx" +...+212 +00 +1. 360" + en
9. Using theorem 12.3, find the three angles of the triangle with vertices P (1,0,-1), Q = (3,-2,0), and R (1,3, 3). a b 2 cose
9. Using theorem 12.3, find the three angles of the triangle with vertices P (1,0,-1), Q = (3,-2,0), and R (1,3, 3). a b 2 cose
5. For parts (a)-(d) below, consider the set of vectors B = {(1,2), (2, -1)}. (a) (2 points) Demonstrate that B is an orthogonal set in the Euclidean inner product space R2. (b) (3 points) Use the set B to create an orthonormal basis in the Euclidean inner product space R2 (e) (7 points) Find the transition matrix from the standard basis S = {(1,0),(0,1)} for R2 to the basis B. Show all steps in your calculation. (d) (7 points)...
(b) Find the area of the triangle PQR.
Find the volume of the parallelepiped with adjacent edges PQ,
PR, and PS. P(−2, 1, 0), Q(3, 5, 3), R(1, 4, −1), S(3, 6, 2)
9. +5/10 points | Previous Answers SCalcET8 12.4.029 Consider the points below. (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. 〈0.16,-8) (b) Find the area of the triangle PQR. Need Help? Read It Watch It Talk to a Tutor...
Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle between v and w. (b) Consider the projection proj, w of w onto v, and then project this projection on u to get proju (proj, w). Is this necessarily equal to the projection proj, w of w on u? Prove or give a counterexample. (c) Find the volume of the parallelepiped with edges formed by u-(2,5,c), v (1,1,1) and w...
T:R3 → R2 is a linear transformation with T(1,0, 2) = (2, -1) and T(0,1, -1) = (5,2). It follows that T(2, -3, 7) is equal to Select one: 0 a. (7,1) O O b. not enough information is given to determine the answer C. (-11, –8) O d. (2, -3) o e. (19,-4)
Let the vectors a = <1,2,3>, b= <1,1, 1 > and c = <1,2, 1 > a) Determine whether the three are coplanar None of these 4 0.71 0.74 no b) Find the volume of the parallelepiped form c) Find the unit vector orthogonal to both ved d) Find the angle between the vectors a and 22.26 bunded to 2 decimal points) 12:21 e) Find the component of the vector a along 39.51 -1 ge
b. Find the volume of the parallelepiped spanned by the vectors (t, 0,0), (1,2,-4), (0, t,-1). For what values of t will there be a zero volume? What can you say about the three vectors when the volume is zero? Using a 3D graphing program, include two graphs of the three vector, one where the volume is not zero and one where the volume is zero. (9pts)
b. Find the volume of the parallelepiped spanned by the vectors (t, 0,0),...
Consider the parallelepiped shown in the figure. The side lengths are l |B1 = 2 and | = 1. The angle between C and bis 60°, the angle between ā and č is 0 = 60° and a makes an angle a of the base plane 30° with respect to the normal 1 h base d. Write down the formula ax + By + yz = d of the body diagonal plane formed by the end points of the three...
T:R R2 is a linear transformation with T(1,0, 2) = (2, 1) and T(0,1,-1) = (-5,2). It follows that T(2, -3,7) is equal to Select one: 0 a. (-11, -8) O b. (2, 3) c (19, -1) d. not enough information is given to determine the answer e(-3,3)