Question

Consider the parallelepiped shown in the figure. The side lengths are l |B1 = 2 and | = 1. The angle between C and bis 60°, the angle between ā and č is 0 = 60° and a makes an angle a of the base plane 30° with respect to the normal 1 h base d. Write down the formula ax + By + yz = d of the body diagonal plane formed by the end points of the three vectors ā, b, and ë.

Answer 1

L eiTers Lies X-axis Al andl the Comman iniho PoriniuTo a omd Onigin in the Than X, y ond z axes X as shaun, fom ghr horded 6 B Corordrate Gin Ia , Iel-1 60 8=60 and angle forrmeel by a with he ueshrt Also eguat 30' thal Condaun phoe find the eguale Ainy) GABC (fomnal by me We nudl & nd Ghe Sn bo Cor 60 ER Cos?Sin Norw an unil veetors alony X, y arcl z are rupdtialy) where lal=a= 2 a Corfp SiabaCosn Sin 6o' i a Cosp Cost? a Ces 66 2 Cos 6' Cos 66 3 k Nex CA = a-ak

and xi yzk be the vecler of parnt P in Ld Y panthon plane Contlaining AABC. the Thun, PBB--x)? - yf- tk Now (Ch)x (CB) i lo the plane Contauriny The veelors X AABC CA and Containedl in me plane Conianiry OABC PB Cund (Pt). [tc x (ca)] (P).4k x( ] Y (PE). 313 (2-x)31 y (mat ialact throuyho by3) (a-x) - 3y X- C=1.0-he 0.そ = 2 Reguird eguiali Ans plane fomod be enel pors x+ 18y ineleperetan me Phe thre vreors a' oral which tniplies thai this plone bo parellal to (Equasnim

and xi yzk be the vecler of parnt P in Ld Y panthon plane Contlaining AABC. the Thun, PBB--x)? - yf- tk Now (Ch)x (CB) i lo the plane Contauriny The veelors X AABC CA and Containedl in me plane Conianiry OABC PB Cund (Pt). [tc x (ca)] (P).4k x( ] Y (PE). 313 (2-x)31 y (mat ialact throuyho by3) (a-x) - 3y X- C=1.0-he 0.そ = 2 Reguird eguiali Ans plane fomod be enel pors x+ 18y ineleperetan me Phe thre vreors a' oral which tniplies thai this plone bo parellal to (Equasnim