IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

sriram.a

the corner of the square OPQR is folded up so that the plame OPQ is perpendicular to plane OQR.The angle between OP&QR is

PRATHAB

its a pi/3

indr12365

I seems 2pi/3
I just imagined with a paper cut

srujana

$Let\ the\ edge\ length\ be\ 2\ units$

$Let\ O(0,0,0)\ be\ the\ Origin$

$R(2,0,0)\\Q(2,2,0)$

$before\ folding,the\ coordinates\ of\ P(0,2,0).$

$after\ folding,\ the\ plane\ OQP\ is\ perpendicular\ to\ the\ plane\ OQR$

$the\ new\ coordinates\ of\ P\ are\ (1,1,\sqrt{2})$

$[To\ get\ the\ coordinates\ of\ P$

$drop\ perpendiculars\ from\ P\ to\ xy\ and\ yz\ planes$

$and\ then\ find\ the\ distance\ of\ the\ foot\ of\ perpendiculars\ from\ the \ x,y,z\ axes$

$which\ will\ give\ their\ respective\ x,y,z\ coordinates]$

$position\ vector\ of\ OP=i+j+\sqrt{2}k$

$position\ vector\ of\ QR=-2j$

$using\ the\ dot\ product, cos \theta=-1/2$

$hence, \theta=2 \pi/3$