If the sum of the unit vectors `hat(a)` and `vec(b)` is a unit vector. Show that the magnitude of their difference is `sqrt(3)`.

The unit vector bisecting vec(OY) and vec(OZ) is

If veca is a non-zero vector of magnitude a and vec(lamda a) a is a unit vector, find the value of lamda

If vec a and vec b are unit vectors such that theta is the angle between then, |vec a - vec b| =

If vec a and vec b are unit vectors such that |vec a + vec b| =1, then |vec a - vec b| =

If vec a and vec b are unit vectors and theta is the angle between them, then |vec a + vec b| =

If vec a and vec b are unit vectors |vec a xx vec b| =1 then the angle between vec a and vec b is

The scalar product of the vector vec(a) = hat(i) + hat(j) + hat(k) with a unit vector along the sum of vectors vec(b) = 2hat(i) + 4hat(j) - 5hat(k) and vec(c ) = lambda hat(i) + 2hat(j) + 3hat(k) is equal to one. Find the value of lambda and hence find the unit vector along vec(b) + vec(c ) .