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Maths-

General

Easy

Question

A square PQRS is folded along the diagonal PR so that the planes PRQ and PRS are perpendicular to one another then the shortest distance between PQ ' and RS interms of P (the length of side of the square) (Q → Q' after folding)

P
$\frac{P}{\sqrt{2}}$
$\sqrt{2} P$
$2 P$

The correct answer is: $fraction numerator P over denominator square root of 2 end fraction$

Let new positing Q be Q'
Let $stack i with rightwards arrow on top comma stack j with rightwards arrow on top comma stack k with rightwards arrow on top$ denote unit vector along PQ '
$text Let end text stack O P with rightwards arrow on top equals O$
$text P.V. of end text Q to the power of ´ end exponent text be end text p stack i with rightwards arrow on top$
$text P.V. of end text R text be end text p stack i with rightwards arrow on top plus p stack j with rightwards arrow on top$
$text P.V. of end text S text be end text p stack k with rightwards arrow on top$
$table row cell E q text end text text o end text text f end text text end text stack P Q with rightwards arrow on top end cell row cell stack r with rightwards arrow on top equals t p stack i with rightwards arrow on top end cell end table$
$table row cell text end text text E end text text q end text text end text text o end text text f end text text end text R S invisible function application stack r with rightwards arrow on top equals p stack i with rightwards arrow on top plus p stack j with rightwards arrow on top plus t left parenthesis p stack i with rightwards arrow on top plus p stack j with rightwards arrow on top minus p stack k with rightwards arrow on top right parenthesis text end text text. end text text end text end cell row cell text end text text r end text text e end text text q end text text u end text text i end text text r end text text e end text text d end text text end text text s end text text h end text text o end text text r end text text t end text text e end text text s end text text t end text text end text text d end text text i end text text s end text text t end text text a end text text n end text text c end text text e end text text end text end cell end table$
$equals open vertical bar fraction numerator left parenthesis p stack i with rightwards arrow on top plus p stack j with rightwards arrow on top right parenthesis times p stack i with rightwards arrow on top cross times left parenthesis p stack i with rightwards arrow on top plus p stack j with rightwards arrow on top minus p stack k with rightwards arrow on top right parenthesis over denominator vertical line p stack i with rightwards arrow on top plus left parenthesis p stack i with rightwards arrow on top plus p stack j with rightwards arrow on top minus p stack k with rightwards arrow on top right parenthesis vertical line end fraction close vertical bar equals fraction numerator p over denominator square root of 2 end fraction$

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