Verified answer

Ответ:

Пошаговое объяснение:

AB = (0-5; 9 + 10; -1-1) = (-5; 18; -2) = -5i + 18k - 2j

|AB| = √(25 + 324 + 4) = √353

2.

a + b = (-5; 9; -3)

a - b = (-5; -3; 5)

3a = (-15; 9; 3)

0,5b = (0; 3; -2)

5a - 3b = (-25; 15; 5) - (0; 18; -12) = (-25; -3; 17)

3.

1) |AB| = √(64 + 36 + 4) = √104 = 2√26

|BC| = √(256 + 16 + 64) = √336 = 4√21

|AC| = √(64 + 100 + 36) = √200 = 10√2

P = 2√26 + 4√21 + 10√2

2) середина BC M(2; 4; -1)

AM = √(0+64+4) = √68 = 2√17

3) AB = (-8; 6; 2)

CA = (-8; -10; 6)

AB * CA = 64 + 60 + 12 = 136

4) AC = (8; 10; -6)

BC = (16; 4; -8)

cosφ = AC * BC/(|AC|*|BC|) = (128 + 40 + 48)/(10√2 * 4√21) = 216/10√42 =

= 216√42/420 = 18√42/35

φ = arccos(18√42/35)