Pertanyaan

Jika nilai ∣ u ⇀ ∣ = 6 , ∣ v ⇀ ∣ = 10 , dan tangen sudut antara vektor u ⇀ dan v ⇀ adalah 3 4 , hasil u ⇀ ⋅ v ⇀ adalah ....

Jika nilai $∣ u ⇀ ∣ = 6, ∣ v ⇀ ∣ = 10,$ dan tangen sudut antara vektor $u ⇀$ dan $v ⇀$ adalah $\frac{4}{3}$ , hasil $u ⇀ \cdot v ⇀$ adalah ....

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

hasil adalah .

hasil

u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top

adalah

Pembahasan

Untuk menentukan hasil , kita bisa gunakan rumus Diketahui: Menentukan sisi miring, dengan Pythagoras. Misalkan: adalah sisi miring. Sehingga, cosinus sudutantara vektor dan : Menentukan hasil . Jadi,hasil adalah .

Untuk menentukan hasil u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top , kita bisa gunakan rumus

$cos space alpha equals fraction numerator u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top over denominator open vertical bar u with rightwards harpoon with barb upwards on top close vertical bar open vertical bar v with rightwards harpoon with barb upwards on top close vertical bar end fraction$

Diketahui: tan space alpha equals 4 over 3

tan space alpha equals depan over samping

Menentukan sisi miring, dengan Pythagoras.

Misalkan: adalah sisi miring.

table attributes columnalign right center left columnspacing 0px end attributes row r equals cell square root of 4 squared plus 3 squared end root end cell row blank equals cell square root of 16 plus 9 end root end cell row blank equals cell square root of 25 end cell row blank equals 5 end table

Sehingga, cosinus sudut antara vektor u with rightwards harpoon with barb upwards on top dan v with rightwards harpoon with barb upwards on top :

cos space alpha equals samping over miring equals 3 over 5

Menentukan hasil u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top .

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space alpha end cell equals cell fraction numerator u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top over denominator open vertical bar u with rightwards harpoon with barb upwards on top close vertical bar open vertical bar v with rightwards harpoon with barb upwards on top close vertical bar end fraction end cell row cell 3 over 5 end cell equals cell fraction numerator u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top over denominator 6 times 10 end fraction end cell row cell 3 over 5 end cell equals cell fraction numerator u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top over denominator 60 end fraction end cell row cell 5 open parentheses u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top close parentheses end cell equals cell 3 times 60 end cell row cell 5 open parentheses u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top close parentheses end cell equals 180 row cell u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top end cell equals cell 180 over 5 end cell row cell u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top end cell equals 36 end table$

Jadi, hasil u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top adalah .

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

5.0 (4 rating)

Pertanyaan serupa

Diketahui vektor u = ⎝ ⎛ 2 − 1 1 ⎠ ⎞ dan v → = ⎝ ⎛ 7 0 1 ⎠ ⎞ . Tentukan sudut antara u dan v .

5.0

Jawaban terverifikasi

Diketahui vektor-vektor u = b i − 12 j + a k dan v = a i + a j − b k . Sudut antara vektor u dan v adalahθ dengan cos θ = 4 3 · Proyeksi vektor pada adalah p = − 4 i − 4 j + 4 k . Nilai da...

4.5

Jawaban terverifikasi

Carilah nilai cosinus sudut yang dibentuk oleh setiap pasangan vektor berikut. b. p = 3 i + 2 j − 6 k dan q = 4 i − 3 j + k

4.5

Jawaban terverifikasi

Diketahui vektor a = ( 2 , − 3 , 3 ) dan b = ( 3 , − 2 , − 4 ) . Besar sudut antara a dan b adalah ....

496

4.9

Jawaban terverifikasi

Diketahui ∣ a ∣ = 5 dan ∣ b ∣ = 12 , sudut antara vektor a dan b adalah 6 0 ∘ , hitunglah a ⋅ b !

136

4.5