(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]| .

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 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.

If vec a=2 hat i-3 hat j+ hat k , hat 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) and ( vec b+ vec c) .

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)

The length of the longer diagonal of the parallelogram constructed on 5 vec a+2 vec b\ a n d\ vec a-3 vec b\ if it is given that | vec a|=2sqrt(2),\ | vec b|=3 and angle between vec a\ a n d\ vec b\ i s pi//4 is a. 15 b. sqrt(113) c. sqrt(593) d. sqrt(369)

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

Prove that the area of a parallelogram with sides vec(A) and vec(B) " is " vec(A) xx vec(B)

If vec a\ a n d\ vec b represent two adjacent sides of a parallel then write vectors representing its diagonals.

Write the equation of the plane containing the lines vec r= vec a+lambda vec b\ a n d\ vec r= vec a+mu vec c