If ` vec p` and ` vec q` are unit vectors forming an angle of `30^0;` find the area of the parallelogram having ` vec a= vec p+2 vec q` and ` vec b=2 vec p+ vec q` is its diagonals.

(22) if vec p and vec q are unit vectors forming an angle of 30^@ ; find the area of the parallelogram having veca=vecp+2vecq and vecb=2vecp+vecq as its diagonals. (23) For any two vectors vec a and vec b , prove that | vec a xxvec b|^2=| [vec a* vec a ,vec a*vec b],[ vec b* vec a, vec b* vec b]| .

Find the angle between two vectors vec a and vec b , if | vec a xx vec b|= vec a . vec b .

If vec a and vec b are two vectors of the same magnitude inclined at an angle of 30^0 such that vec adot vec b=3, find | vec a|,| vec b| .

If vec a=2 hat i-3 hat j+ hat k ,\ vec b=- hat i+ hat k ,\ vec c=2 hat j- hat k are three vectors find the area of the parallelogram having diagonals ( vec a+ vec b)\ a n d\ ( vec b+ vec c)dot

If vec a ,\ vec b ,\ vec c are unit vectors such that vec a+ vec b+ vec c= vec0 find the value of vec adot vec b+ vec bdot vec c+ vec cdot vec adot'

If vec a , vec b , vec c are unit vectors such that vec a+ vec b+ vec c= vec0, then write the value of vec a . vec b+ vec b . vec c+ vec c . vec a

vec a , vec b , vec c are unit vectors such that vec a+ vec b+ vec c=0. then find the value of vec a. vec b+ vec b.vec c+ vec c. vec a

If vec(a) and vec(b) are the unit vectors and theta is the angle between them, then vec(a) + vec(b) is a unit vector if

If vec p is a unit vector and ( vec x-\ vec p).( vec x+\ vec p)=80 , then find | vec x|

If vectors vec a and vec b are two adjacent sides of a parallelogram, then the vector respresenting the altitude of the parallelogram which is the perpendicular to veca is a. vec b+( vec bxx vec a)/(| vec a|^2) b. ( vec a. vec b)/(| vec b|^2) c. vec b-(( vec b. vec a)veca)/(| vec a|^2) d. ( vec axx( vec bxx vec a))/(| vec b|^2)