IIT JEE , AIEEE Forum - Mathematics , Algebra

man111

(1) let a is a unit vector and 1<=c<=sqrt(6), and a+a*b = c, Then find the maximum volume of parallopiped,

if a,b,c are the edge of parallopiped.

little_genius

a + aXb =c
a.c + (aXb).c = |c|^2
or, (aXb).c= |c|^2- a.c= |c|^2 - |c|cos@ ..
where @ is the angle b/w a and c.
now for @ tending to 180 degrees we and maxising the value of c as rt6 we get the max volume.
so max volume=(aXb).c= 6 -(-rt6)= 6+rt6...

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