Question

Срочно, Геометрия векторы

Answer 1

а) 2a+3b = (2*2+3*6, 2*3+3*4, 2*1+3*7) = (22, 18, 23)
|2a+3b| = sqrt (22^2+18^2+23^2) = sqrt (1337)

2) 4c-a = (4*2-2, 4*8-3, 4*3-1) = (6, 29, 11)
|4c-a| = sqrt(998)

3) 2b-c = (2*6-2, 2*4-8, 2*7-3) = (10, 0, 11)
|2b-c| = sqrt (221)

4) (2a+c)*(3b-a) = (2*2+2, 2*3+8, 2*1+3)*(3*6-2, 3*4-3, 3*7-1) = (6, 14, 5)*(16, 9, 20) = 6*16 + 14*9+5*20 = 322

5) cos (2b+c, 4a-b) = cos( (2*6+2, 2*4+8, 2*7+3), (4*2-6, 4*3-4, 4*1-7) = cos ((14, 16, 17), (2,8,-3))
|2b+c| = sqrt (741)
|4a-b| = sqrt (77)

cos(2b+c, 4a-b) = (14*2+16*8-17*3)/(sqrt(741)*sqrt (77)) = 105/(sqrt (741)*sqrt (77))