Consider a tetrahedron with faces `f_1, f_2, f_3, f_4`. Let `vec a_1, vec a_2, vec a_3, vec a_4` be the vectors whose magnitudes arerespectively equal to the areas of `f_1,f_2,f_3,f_4` and whose directions are perpendicular to these faces in theoutward direction. Then

Consider a tetrahedron with faces F_(1),F_(2),F_(3),F_(4) . Let vec(V_(1)), vecV_(2),vecV_(3),vecV_(4) be the vectors whose magnitude are respectively equal to areas of F_(1).F_(2).F_(3).F_(4) and whose directions are perpendicular to their faces in outward direction. Then |vecV_(1) + vecV_(2) + vecV_(3) + vecV_(4)| , equals:

Consider a tetrahedron with faces F_(1),F_(2),F_(3),F_(4) . Let vec(V_(1)), vecV_(2),vecV_(3),vecV_(4) be the vectors whose magnitude are respectively equal to areas of F_(1).F_(2).F_(3).F_(4) and whose directions are perpendicular to their faces in outward direction. Then |vecV_(1) + vecV_(2) + vecV_(3) + vecV_(4)| , equals:

Let A be the set of 4-digit numbers a_1 a_2 a_3 a_4 where a_1 > a_2 > a_3 > a_4 , then n(A) is equal to

Let A be the set of 4-digit numbers a_1 a_2 a_3 a_4 where a_1 > a_2 > a_3 > a_4 , then n(A) is equal to

Let A be the set of 4-digit numbers a_1 a_2 a_3 a_4 where a_1 > a_2 > a_3 > a_4 , then n(A) is equal to

Let A be the set of 4-digit numbers a_1 a_2 a_3 a_4 where a_1 > a_2 > a_3 > a_4 , then n(A) is equal to

Consider a vector vec(F)= 4hat(i)-3hat(j) . Another vector that is perpendicular to vec(F) is

In a four-dimensional space where unit vectors along the axes are hat i , hat j , hat k and hat l , and vec a_1, vec a_2, vec a_3, vec a_4 are four non-zero vectors such that no vector can be expressed as a linear combination of others and (lambda-1)( vec a_1- vec a_2)+mu( vec a_2+ vec a_3)+gamma( vec a_3+ vec a_4-2 vec a_2)+ vec a_3+delta vec a_4=0, then