dx |
回覆於: 2013/2/27 上午 07:16:52
1.xy平面法向量n(0,0,1) ;3x-2y+z+1=0法向量m(3,-2,1) 其夾角φ則φ=180°-θ |n|=1;|m|=√14 => n dot m=√14 *cosφ=1 => cosφ=1/√14 => sinφ=sinθ=√13/√14
2E包含z軸: ax+by=0 法向量(a,b,0);E1:x+2y-2z=0法向量(1,2,-2); =>(a,b,0)dot(1,2,-2)=a+2b=√(a^2+b^2) *3*cosθ=±√(a^2+b^2) =>a^2+4ab+4b^2=a^2+b^2 => 4ab+3b^2=0=b(4a+3b) => b=0 or a:b=3:-4 => 方程 ax=0 or 3x-4y=0 3. ax+cz=0法向量(a,0,c),xy平面法向量(0,0,1), =>(a,0,c)dot(0,0,1)=√(a^2+c^2) *cos45°=c =>(a^2+c^2 )*0.5=c^2 => a^2+c^2=2c^2 => a^2=c^2 => a=c or a=-c =>法向量 (1,0,1) ;(1,0,-1)=> 方程 x+z=0 or x-z=0
|