Question

If `overset(to)(a) , overset(to)(b) , overset(to)(c ) ` are non-coplanar unit vectors such that
`overset(to)(a) xx (overset(to)(b) xx overset(to)(c )) = ((overset(to)(b) + overset(to)(c )))/(sqrt(2))`, then the angle between `overset(to)(a) " and " overset(to)(b)` is
A. `(3pi)/(4)`
B. ` (pi)/(4)`
C. `(pi)/(2)`
D. `pi`

Answer 1

Correct Answer - A
Since `vec(a) xx (vec(b) xx vec(c )) = (vec(b) + vec(c ))/(sqrt(2))`
` rArr (vec(a) " ." vec(c )) vec(b) - (vec(a) ". " vec(b)) vec(c ) = (1)/(sqrt(2)) vec(b) + (1)/(sqrt(2)) vec( c)`
On equating the coefficient of `vec(c )` we get
`rArr |vec(a)||vec(b)|| cos 0 = (1)/(sqrt(2))`
` :. cos 0 = (1)/(sqrt(2)) rArr 0= (3pi)/(4)`