A unit vector ` vec r` makes angle `pi/3\ a n d\ pi/2` with ` hat j a n d\ hat k` respectively and an acute angle `theta\ w i t h\ i ,` Find `thetadot`

A unit vector vec a makes angles pi/4\ a n d\ pi/3 with hat i\ a n d\ hat j respectively and an acute angle theta with hat kdot Find the angle theta and components of vec adot

If a unit vector vec a makes an angle pi/3 with hat i ,\ pi/4 with hat j and an acute angle theta with hat k then find theta and hence, the components of vec a .

If a unit vector vec a makes angle pi//3 with hat i ,pi//4 with hat j and an acute angle theta with hat k , then find the components of vec a and the angle thetadot

If a unit vector vec a makes angles pi/3 with hat i ,pi/4 with hat j and an acute angle theta with hat k , then find the value of theta .

In sub-parts (i) and (ii) choose the correct option and in sub-parts (iii) to (v), answer the questions as instructed. If a unit vector hat(a) makes angle pi/3 with hat(i), pi/3" with " hat(j) and an acute angle theta with k, then find theta .

If a unit vector vec(a) makes a angle (pi)/(3) with hat(i), (pi)/(4) with hat(k) and an acute angle q with hat(j) then find the value of q.

If a unit vector vec(a) makes angle (pi)/(3) with hat(i), (pi)/(4) with hat(j) and theta in ((pi)/(2), pi) with hat(k) then a value of theta is (k pi)/(l) (k and l are coprime). The value of k is _________.

The position vectors of the vertices A ,B ,a n dC of a triangle are hat i+ hat j , hat j+ hat ka n d hat i+ hat k , respectively. Find the unite vector hat r lying in the plane of A B C and perpendicular to I A ,w h e r eI is the incentre of the triangle.

If the vectors hat(i)+hat(j)+hat(k) makes angle alpha, beta and gamma with vectors hat(i), hat(j) and hat(k) respectively, then

Dot products of a vector with vectors hat i- hat j+ hat k ,\ 2 hat i+ hat j-3 hat k\ a n d\ hat i+ hat j+ hat k are respectively 4, 0 and 2. Find the vector.