In a quadrilateral `A B C D , vec A C` is the bisector of ` vec A Ba n d vec A D` , angle between ` vec A Ba n d vec A D` is `2pi//3` , `15| vec A C|=3| vec A B|=5| vec A D|dot` Then the angle between ` vec B Aa n d vec C D` is `(a) cos^(-1)(sqrt(14)/(7sqrt(2)))` b. `cos^(-1)(sqrt(21)/(7sqrt(3)))` c. `cos^(-1)(2/(sqrt(7)))` d. `cos^(-1)((2sqrt(7))/(14))`

Let vec a , vec ba n d vec c be unit vectors, such that vec a+ vec b+ vec c= vec x , vec a dot vec x=1, vec b dot vec x=3/2,| vec x|=2. Then find the angle between vec c and vec x

If vec a\ a n d\ vec b are two vectors such that | vec axx vec b|=sqrt3\ a n d\ vec adot vec b=1, find the angle between vec a\ a n d\ vec b .

Given vec(C )= vec(A) xx vec(B) and vec(D) = vec(B) xx vec(A) . What is the angle between vec(C ) and vec(D) ?

ABCDE is a pentagon. Prove that the resultant of force vec A B , vec A E , vec B C , vec D C , vec E D and vec A C ,is 3 vec A C .

If vec aa n d vec b are any two vectors of magnitudes 1 and 2, respectively, and (1-3 vec a . vec b)^2+|2 vec a+ vec b+3( vec axx vec b)|^2=47 , then the angel between vec aa n d vec b is pi//3 b. pi-cos^(-1)(1//4) c. (2pi)/3 d. cos^(-1)(1//4)

If vec aa n d vec b are two vectors of magnitude 1 inclined at 120^0 , then find the angle between vec ba n d vec b- vec adot

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 the two adjacent sides of two rectangles are represented by vectors vec p=5 vec a-3 vec b ; vec q=- vec a-2 vec b \ and \ vec r=-4 vec a- vec b ; vec s=- vec a+ vec b , respectively, then the angel between the vector vec x=1/3( vec p+ vec r+ vec s) \ and \ vec y=1/5( vec r+ vec s) is a. -cos^(-1)((19)/(5sqrt(43))) b. cos^(-1)((19)/(5sqrt(43))) c. pi-cos^(-1)((19)/(5sqrt(43))) d. cannot be evaluate

If vec | a| = sqrt(3) , |vec(b)| = 2 and vec(a) . vec(b) = sqrt(6) , then find angle between the vectors vec(a) and vec(b)

If vec a , vec b ,a n d vec c are such that [ vec a vec b vec c]=1, vec c=lambda vec axx vec b , , | vec a|=sqrt(2),| vec b|=sqrt(3)a n d| vec c|=1/(sqrt(3)) , then the angle between vec a and vec b is pi/6 b. pi/4 c. pi/3 d. pi/2