Question

No 7,sama 8. pakai cara ya

Answer 1

Verified answer

Vektor , Kelas 10

7)

a = -i + j + 2k
b = i - j + 2k

a + b = 4k
a - b = -2i - 2j


|a + b| = √4² = 16
| a - b | = √(-2)² + (-2)² = √8 = 2√2

misal saja a + b = u
dan a - b = v

maka

u . v = (-2)(0) + (-2)(0) + 4(0) = 0
|u||v| cos alfa = 0
16 . 2√2 . cos alfa = 0
cos alfa = 0/32√2
cos a = 0
alfa = arc cos 0 = 90°

8)

a = 2i - 4j + 4k
b = 3i + 2j + 6k

sin alfa?

a . b = (2)(3) + (-4)(2) + (4)(6)
= 6 - 8 + 24
= 22

|a| = √4+16+16 = √36 = 6
|b| = √9+4+36 = √49 = 7

cos a = (a . b ) / (|a||b|)
cos a = (22)/(6)(7)
cos a = (22/42) = 11/21

cos = sa /mi
sa = 11
mi = 21
de = √(21²-11²)
= √441 - 121
= √320
= 8√5

sin a = de/mi
= (8√5) / 21

A