# Dana coordinate of tops of a pyramid of ABCD. And (0;0;6), B(1;3;-1), C(4;-1;-3). To calculate: 1) Pyramid volume; 2) AB edge length; 3) Area of a side; HELP PLEASE

Izot

325

A) 1. Finding of lengths of edges and coordinates vektorovxyzdlina rebravektorav = {to xB-xA, yB-yA, zB-zA } 2012.236067977VektorVS= {to xC-xB, yC-yB, zC-zB }-10-33.16227766VektorAS= {to xC-xA, yC-yA, zC-zA } 10-22.236067977VektorAS= {to xS-xA, yS-yA, zS-zA } 3-2-13.741657387ВекторBS= {to xS-xB, yS-yB, zS-zB } 1-2-23ВекторCS= {to xS-xC, yS-yC, zS-zC } 2-213 the Volume of a pyramid is equal: of (AB {x1, y1, z1 }; AC {x2, y2, z2 }; AS {x3, y3, z3 }) = x3 · a1+y3 · a2+z3 · a3. the Work of vectors a × b = {ay*bz - az*by; az*bx - ax*bz; ax*by - ay*bx }. pyramid Volume: x yz AB*AC: 0 50, V = (1/6) * 10 = 1.6666667. b) length of height lowered on AVS basis: H=3V/Sosn Height lowered on a side of ABC is equal: 2. to d Distance from M1 point (x1; y1; z1) to the plane Ax + By + Cz + D = to 0 equally absolute value of size: AVS plane Equation: y-1 = 0. c) the equation of the plane passing through points And, In, With: AVS plane equation: y-1 = 0. Equation of the planes of sides. Let (h1, h2, h3), (u1, u2, u3) and (z1, z2, z3) – coordinates of the first, second itrety point respectively. (x-x1) * (u2-u1) * (z3-z1) – (x-x1) * (z2-z1) * (y3-y1) – (y-y1) * (x2-x1) * (z3-z1) + (y-y1) * (z2-z1) * (x3-x1) + (z-z1) * (x2-x1) * (y3-y1) – (z-z1) * (y2-y1) * (x3-x1) = 0. of Uravneniyeploskosti of a side of ABC: of X-x100yy1-41zz100005-500 0x+5y+0z+-5=0 After reduction on 5, we receive AVS: at - 1 = 0. d) a corner between a straight line HELL and the AVS plane: sinusradian degree 10 3.741657 518.70829 0.534522 0.563943 32.31153 e) a corner between direct AV and the EXPERT: of of AC*AB |AC*AB| cos αрадианградусы of sin α 05 0 1.570796 90 1

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