Pertanyaan

Diketahui p ⇀ = ⎝ ⎛ − 3 3 0 ⎠ ⎞ dan q ⇀ = ⎝ ⎛ 1 3 − 2 ⎠ ⎞ . Apabila α adalah sudut yang dibentuk antara vektor p ⇀ dan q ⇀ , maka tan α = ....

$Diketahui p ⇀ = ⎝ ⎛ - 3 30 ⎠ ⎞ dan q ⇀ = ⎝ ⎛ 13 - 2 ⎠ ⎞ . Apabila α adalah sudut yang dibentuk antara vektor p ⇀ dan q ⇀, maka tan α = ....$

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F. Pratama

Master Teacher

Mahasiswa/Alumni Universitas Putra Indonesia YPTK Padang

Jawaban terverifikasi

Pembahasan

$Ingat space rumus space perkalian space titik space pada space vektor colon p with rightwards harpoon with barb upwards on top. q with rightwards harpoon with barb upwards on top equals open vertical bar p with rightwards harpoon with barb upwards on top close vertical bar open vertical bar q with rightwards harpoon with barb upwards on top close vertical bar space cos space straight alpha open parentheses table row cell negative 3 end cell row 3 row 0 end table close parentheses open parentheses table row 1 row 3 row cell negative 2 end cell end table close parentheses equals square root of left parenthesis negative 3 right parenthesis squared space plus space 3 squared end root square root of 1 squared plus 3 squared plus left parenthesis negative 2 right parenthesis squared end root space cos space straight alpha minus 3 plus 9 plus 0 equals square root of 18 square root of 14 cos space straight alpha 6 equals square root of 252 space cos space straight alpha 6 equals 6 square root of 7 space cos space straight alpha Berarti comma space cos space straight alpha space equals space fraction numerator 6 over denominator 6 square root of 7 end fraction equals fraction numerator 1 over denominator square root of 7 end fraction sin space straight alpha space equals space fraction numerator square root of left parenthesis square root of 7 right parenthesis squared minus 1 squared end root over denominator square root of 7 end fraction equals fraction numerator square root of 6 over denominator square root of 7 end fraction tan space straight alpha space equals fraction numerator begin display style fraction numerator square root of 6 over denominator square root of 7 end fraction end style over denominator begin display style fraction numerator 1 over denominator square root of 7 end fraction end style end fraction equals square root of 6$