[{"data":1,"prerenderedAt":21},["ShallowReactive",2],{"formula-en-force-magnitude-three-components":3},{"formula":4,"related_topics":13,"alternates":18},{"id":5,"code":6,"slug":7,"title":8,"formula":9,"locale":10,"seo_title":11,"seo_description":11,"content_html":12},157,"statics-force-magnitude-3d","force-magnitude-three-components","Force Magnitude from Three Components","F = √(Fₓ² + Fᵧ² + F_z²)","en",null,"\u003Cp>If a three-dimensional force is specified by its Cartesian components $F_x$, $F_y$, and $F_z$, its magnitude is:\u003C\u002Fp>\u003Cp>$$F=\\sqrt{F_x^2+F_y^2+F_z^2}.$$\u003C\u002Fp>\u003Cp>The components are algebraic quantities whose signs determine the vector direction, while the force magnitude is always nonnegative.\u003C\u002Fp>\u003Cdiv data-formula-calculator-config=\"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\">\u003C\u002Fdiv>",[14],{"id":15,"name":16,"path":17},191,"Three-Dimensional Force Systems","theoretical-mechanics\u002Fstatics\u002Fthree-dimensional-statics\u002Fthree-dimensional-force-systems",{"en":19,"uk":20},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Fformulas\u002Fforce-magnitude-three-components","https:\u002F\u002Fmechclassroom.com\u002Fformulas\u002Fmodul-syly-za-troma-proektsiiamy",1787712543187]