Question

Terserah mau jawab no brp saja

Answer 1

(13)
a tegak lurus b, maka

(-1)(-2) + (2)(2p) + (-1)(6) = 0
2 + 4p - 6 = 0, diperoleh nilai p = 1
jadi vektor b adalah -2i + 2j + 6k
diminta |a + b| = ?
a + b = (- i + 2j - k) + (- 2i + 2j + 6k) = - 3i + 4j + 5k
sehingga |a + b| = √ [(- 3)² + (4)² + (5)²]

∴ |a + b| = √50 = 5√2

(15)
vector a = 

vector b = 

a.(2a - 3b) = 2|a|² - 3a.b
karena |a| = √ [(2)² + (-3)² + (5)²], maka |a|² = (2)² + (-3)² + (5)² = 38
a.b = (2)(1) + (-3)(3) + (5)(3) = 8

sehingga,
⇔ a.(2a - 3b) = 2|a|² - 3a.b
⇔                   = 2(38) - 3(8)
⇔                   = 52

(18)
Rumus panjang proyeksi vector a pada vector b adalah [a.b] / |b|
 
[a.b] / |b| = 2/3 |b|
[a.b] = 2/3 |b|²

⇔ [(3)(4) + (-1)(-4) + (4)(p + 4)] = 2/3.{√ [(4)² + (-4)² + (p + 4)²]}²

⇔ 16 + 4p + 16 = 2/3.[16 + 16 + (p + 4)²]

⇔ 6p + 48 = 32 + p² + 8p + 16

⇔ p² - 2p = 0

⇔ p(p - 2) = 0

⇔ diperoleh p = 0 atau p = 2

Answer 2

Saya mau jawab no 18
Rumus panjang proyeksi vector a pada vector b adalah [a.b] / |b|
 
[a.b] / |b| = 2/3 |b|
[a.b] = 2/3 |b|²

*  [(3)(4) + (-1)(-4) + (4)(p + 4)] = 2/3.{√ [(4)² + (-4)² + (p + 4)²]}²

*  16 + 4p + 16 = 2/3.[16 + 16 + (p + 4)²]

*  6p + 48 = 32 + p² + 8p + 16

*  p² - 2p = 0

*  p(p - 2) = 0

*  diperoleh p = 0 atau p = 2
maaf kalo salah