If a unit vector `vec(a)` makes an angle `(pi)/(3)` with `hati,(pi)/(4)` sith `hatj` and an acute angle `theta` with `hatk`, then find the component of `vec(a)`.

If a unit vector veca makes angles (pi)/(3) with hati,(pi)/(4) with hatj and an acute angle theta with hatk then find theta and hence , the components of veca .

A unit vector vec(a) is perpendicualr to the vectors hati+2hatj-hatk and 3hati-hatj+hatk then find the components of vec(a) .

vec(a)=2hati-2hatj+hatk,vec(b)=hati+2hatj-2hatk and vec( c )=2hati-hatj+4hatk then find the projection of vec(b)+vec( c ) on vec(a) .

vec(a) and vec(b) are unit vectors and angle between them is pi/k . If vec(a)+2vec(b) and 5vec(a)-4vec(b) are perpendicular to each other then find the integer value of k.

A vector vec(A) of length 10 units makes an angle of 60^(@) with a vector vec(B) of length 6 units. Find the magnitude of the vector difference vec(A)-vec(B) & the angles with vector vec(A) .

Let vec a= hat i be a vector which makes an angle of 120^@ with a unit vector vec b in XY plane. then the unit vector (vec a+ vec b) is

The values of x for which the angle between the vectors veca =xhati - 3hatj-hatk and vecb = 2x hati + x hatj -hatk is acute, and the angle, between the vector vecb and the axis of ordinates is obtuse, are

If vec(e_(1)) and vec(e_(2)) are two unit vectors and theta is the angle between them, then sin (theta/2) is:

Find a unit vector perpendicular to each one of the vectors vec a =4hati -hatj +3hatk and vecb =3 hati +2hatj -hatk