diketahui vektor a=⎝⎛34−5⎠⎞ dan b=⎝⎛1−22⎠⎞. Nilai sinus sudut antara adan b adalah...

Pertanyaan

$diketahui\;vektor\;\overrightarrow a=\begin{pmatrix}3\\4\\-5\end{pmatrix}\;dan\;\overrightarrow b=\begin{pmatrix}1\\-2\\2\end{pmatrix}.\;Nilai\;\sin us\;sudut\;antara\;\overrightarrow adan\;\overrightarrow b\;adalah...$

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

$vertical line a ⃗ vertical line equals square root of 3 squared plus 4 squared plus negative 5 squared right parenthesis end root equals square root of 9 plus 16 plus 25 end root equals square root of 50 equals 5 square root of 2 vertical line b ⃗ vertical line equals square root of 1 squared plus negative 2 squared plus 2 squared right parenthesis end root equals square root of 1 plus 4 plus 4 end root equals square root of 9 equals 3 a ⃗. b ⃗ equals vertical line a ⃗ vertical line. vertical line b ⃗ vertical line c o s space alpha left parenthesis 3 cross times 1 right parenthesis plus left parenthesis 4 cross times left parenthesis negative 2 right parenthesis right parenthesis plus left parenthesis left parenthesis negative 5 right parenthesis cross times 2 right parenthesis equals 5 square root of 2 cross times 3 cross times c o s space alpha space space space space space space space space space space space space space space space space space space minus 15 space space space space space space space space space space space space space space space space space space space space space space space space space space equals 15 square root of 2 space c o s space alpha space c o s space alpha equals negative fraction numerator 1 over denominator square root of 2 end fraction. fraction numerator square root of 2 over denominator square root of 2 end fraction equals negative 1 half square root of 2$

Nilai sudut α yg memenuhi adalah 135^o dan 215^o ( kuadran II dan kuadran III)

Karena sudut antara 2 vektor kurang dari 180^o maka α = 135^o

sin = sin 135^o =