Jawaban:

Kelas 12 Matematika Bab 4 - Vektor

Kata kunci : Panjang proyeksi

Kode soal : 12.2.4 [Bab 4 - Vektor]

Penjelasan dengan langkah-langkah:

a = ( 2, -2, 4 )

lal = √2^2 + (-2)^2 + 4^2

lal = √4+4+16

lal = √24

lal = 2√6

b = (14,-2,p)

lbl = √14^2 + (-2)^2 + p^2

lbl = √196 + 4 + p^2

lbl = √200+p^2

lzl = 8/√5

a·b / lbl = 8/√5

2(14) + (-2)(-2) + 4(p) / √200+p^2 = 8/√5

32 + 4p / √200+p^2 = 8/√5

______________ dibagi 4

8 + p / √200+p^2 = 2/√5

kuadratkan kedua ruas

(p+8)^2 / (200+ p^2) = 4/5

800 + 4p^2 = 5(p^2 + 16p + 64)

800 + 4p^2 = 5p^2 + 80 p + 320

p^2 + 80p + 320 = 800

(p + 40)^2 + 320- 1600 = 800

(p+40)^2 = 1600 + 480

(p+40) = √4080 ~~ 45

p + 40 = 45

p = 5 ✔