Addition Of Vectors

The correct answer is A:

%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D

Given that;
The volume of parallelopiped is given by

%5B%5Cvec%7Ba%7D%5Cspace%5Cvec%7Bb%7D%5Cspace%5Cvec%7Bc%7D%5D

;
Where,

%5Cvec%7Ba%7D%3D%5Chat%7Bi%7D%2Ba%5Chat%7Bj%7D%2B%5Chat%7Bk%7D

%5Cvec%7Bb%7D%3D%5Chat%7Bj%7D%2Ba%5Chat%7Bk%7D

%5Cvec%7Bc%7D%3Da%5Chat%7Bi%7D%2B%5Chat%7Bk%7D

%5Ctherefore

Putting values we can make

%5Cbegin%7Bvmatrix%7D1%26a%261%5C%5C0%261%26a%5C%5Ca%260%261%5Cend%7Bvmatrix%7D

%3D1(1-0)-a(0-a%5E2)%2B1(0-a)

%3D1%2Ba%5E3-a

%5Ctherefore

Volume (v)=

1%2Ba%5E3-a

The question asks for the minimum value of ‘a’
So,

%5Cfrac%7Bdv%7D%7Bda%7D%3D%5Cfrac%7Bd%7D%7Bda%7D(1%2Ba%5E3-a)

⇒

3a%5E2-1%3D0

⇒

3a%5E2%3D1

⇒

a%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D

Chapter Questions
1 MCQs