Let ` vec a , vec b ,a n d vec c` be vectors forming right-hand traid. Let ` vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c]),a n d vec r=( vec axx vec b)/([ vec a vec b vec c]),dot` If `x in R^+,` then
a. `x[ vec a vec b vec c]+([ vec p vec q vec r])/x` has least value `=2`. b. `x^4[ vec a vec b vec c]^2+([ vec p vec q vec r])/(x^2)` has least value `=(3/2)^(2//3)` c. `[ vec p vec q vec r]>0` d. none of these

Options

A. `x [veca vecb vecc] + ([vecp vecqvecr])/x ` has least value 2
B. `x^(2) [veca vecb vecc]^(2) + ([vecp vecqvecr])/x^(2) ` has least value `(3//2^(2//3))`
C. `[vecp vecq vecr] gt 0 `
D. none of these

Answer

a,c

Explanation

we have ` [vecp vecq vecr] = 1/ ([ veca vecb vecc])` therefore,
` [vecp vecq vecr] gt 0`
a. ` x gt 0, x [veca vecb vecc] + ([vecp vecq vecr])/x ge 2`
( using ` A.M. ge G.M.`)
b . Similarly, use `A.M. ge G.M`