If unit vectors ` vec a` and ` vec b` are inclined at angle `2theta` such that `| vec a- vec b|<1a n d0lt=thetalt=pi ,t h e n` `theta` lies in interval a.`[0,pi//6)` b. `(5pi//6,pi]` c. `[pi//6,pi//2]` d. `[pi//2,5pi//6]`

Let vec a* vec b=0,w h e r e vec aa n d vec b are unit vectors and the unit vector vec c is inclined at an angle theta to both vec aa n d vec bdot If vec c=m vec a+n vec b+p( vec axx vec b),(m ,n , p in R), then a. -pi/4lt=thetalt=pi/4 b. pi/4lt=thetalt=(3pi)/4 c. 0lt=thetalt=pi/4 d. 0lt=thetalt=(3pi)/4

If non-zero vectors vec a and vec b are equally inclined to coplanar vector vec c , then vec c can be a. (| vec a|)/(| vec a|+2| vec b|)a+(| vec b|)/(| vec a|+| vec b|) vec b b. (| vec b|)/(| vec a|+| vec b|)a+(| vec a|)/(| vec a|+| vec b|) vec b c. (| vec a|)/(| vec a|+2| vec b|)a+(| vec b|)/(| vec a|+2| vec b|) vec b d. (| vec b|)/(2| vec a|+| vec b|)a+(| vec a|)/(2| vec a|+| vec b|) vec b

Vectors vec a and vec b are non-collinear. Find for what value of n vectors vec c=(n-2) vec a+ vec b and vec d=(2n+1) vec a- vec b are collinear?

Let vec a , vec b ,a n d vec c be non-coplanar unit vectors, equally inclined to one another at an angle theta then [ veca vecb vecc ] in terms of θ is equal to :

If vec aa n d vec b are two vectors and angle between them is theta, then | vec axx vec b|^2+( vec adot vec b)^2=| vec a|^2| vec b|^2 | vec axx vec b|=( vec adot vec b),iftheta=pi//4 vec axx vec b=( vec adot vec b) hat n ,(w h e r e hat n is unit vector, ) if theta=pi//4 ( vec axx vec b)dot( vec a+ vec b)=0

If vec aa n d vec b are two unit vectors incline at angle pi//3 , then { vec axx( vec b+ vec axx vec b)}dot vec b is equal to (-3)/4 b. 1/4 c. 3/4 d. 1/2

If vec a , vec b , vec c are unit vectors such that vec a. vec b=0= vec a. vec c and the angle between vec b and vec c is pi/3, then find the value of | vec axx vec b- vec axx vec c| .

The position vectors of the vertices A ,Ba n dC of a triangle are three unit vectors vec a , vec b ,a n d vec c , respectively. A vector vec d is such that vec d ⋅ vec a = vec d ⋅ vec b = vec d ⋅ vec c a n d vec d=lambda( vec b+ vec c)dot Then triangle A B C is a. acute angled b. obtuse angled c. right angled d. none of these

Let vec a , vec ba n d vec c be pairwise mutually perpendicular vectors, such that | vec a|=1,| vec b|=2,| vec c|=2. Then find the length of | vec a+ vec b+ vec c |

If two vectors vec(a) and vec (b) are such that |vec(a) . vec(b) | = |vec(a) xx vec(b)|, then find the angle the vectors vec(a) and vec (b)