Jika |a|=5√2 |b|=√6 dan |a+b|=√3 nilai |a-b| adalah

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Hasilnya yaitu 13 ,cara agar mendapatkan hasil 13 bagaimana kakk?​

Jika |a|=5√2 |b|=√6 dan |a+b|=√3 nilai |a-b| adalah

Jawab:

Penjelasan dengan langkah-langkah:

|a+b| = sqrt{|a|^2+|b|^2+2|a||b| cos theta}\(sqrt{3})^2 = (5sqrt{2})^2+(sqrt{6})^2+ 2(5sqrt{2})(sqrt{6}) cos theta\3 = 50+6+10sqrt{12} cos theta\-53 = 20sqrt{3} cos theta\cos theta = -frac{53sqrt{3}}{60}\\|a-b| = sqrt{|a|^2+|b|^2-2|a||b| cos theta}\|a-b| = sqrt{50+6-2(5sqrt{2})(sqrt{6})(-frac{53sqrt3}{60})}\|a-b| = sqrt{56+53}\|a-b| = sqrt{109}