Let ||u||_2, d_2(u,v), and partial_2(u,v) denote the Euclidean norm, distance, a
ID: 2896531 • Letter: L
Question
Let ||u||_2, d_2(u,v), and partial_2(u,v) denote the Euclidean norm, distance, and angle, respectively, associated with the dot product u.v, and suppose ||u||, d(u,v), and partial(u,v) are the corresponding quantities associated with the inner product defined on R^3 by = 6u_1 v_1 + 4 u_2 v_2 + 2 u_3 v_3. Find (3,1) . (3,2), || (3, 1) ||_2, || (3, 2) ||_2, d_2 ( (3, 1), (3, 2) ), and partial_2 ( (3,1), (3,2) ) in radians rounded to 5 digits. And for u = (3, 1, -2) and v = (3, 2, -2) in R^3, find u .u, u.v, and v . v and use those values to find u . (-3 u -5 v), ||u||_2, d_2 (u,v), and partial_2 (u,v) in radians rounded to 5 digits. , , and , and use those values to find , ||u||, d(u,v), and partial (u,v) in radians rounder to 5 digits. u times v, and use it to find v times u, u times (-3 u - 5 v), and u . (v times (8, 6, 1) ).Explanation / Answer
b) u =( 3, 1, -2) and v = ( 3, 2 , -2)
b) u.u , u.v and v.v
u.u = ( 3.3 +1.1 -2*-2) = 9 +1+4 = 14; v.v = 3*3 +2*2 -2*-2 = 9 +4 +4 = 17
u.v = 3.3 +1.2 -2.-2 = 9 +2 +4 = 15
u.( -3u -5v) = -3u.u -5u.v = -3(14) -5(15) = -42 -75 = -117
||u||2 = 3^2 +1^2 + 2^2 = 9 +1+4 =14
d2(u, v) = sqrt(( 3-3)^2 + (1-2)^2+ ( -2 +2)^2)
= sqrt( 1 ) = 1unit
cos(theta) = (u.v)/||u.||v|| = 15/(sqrt(14*17)
thet = 0.23393 rad
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