A parallelogram is constructed on the vectors `veca=3vecalpha-vecbeta, vecb=vecalpha+3vecbeta`. If `|vecalpha|=|vecbeta|=2` and angle between `vecalpha and vecbeta is pi/3` then the length of a diagonal of the parallelogram is (A) `4sqrt(5)` (B) `4sqrt(3)` (C) 4sqrt(7)` (D) none of these

If veca is perpendicuar to vecb and vecc |veca|=2, |vecb|=3,|vecc|=4 and the angle between vecb and vecc is (2pi)/3, then [veca vecb vecc] is equal to (A) 4sqrt(3) (B) 6sqrt(3) (C) 12sqrt(3) (D) 18sqrt(3)

If veca is perpendicuar to vecb and vecc |veca|=2, |vecb|=3,|vecc|=4 and the angle between vecb and vecc is (2pi)/3, then [veca vecb vecc] is equal to (A) 4sqrt(3) (B) 6sqrt(3) (C) 12sqrt(3) (D) 18sqrt(3)

If |vecalpha|=|vecbeta|=|vecalpha+vecbeta|=4 , then the value of |vecalpha-vecbeta| is

If vecalpha=3hati-hatk, |vecbeta|=vec(5) and vecalpha.vecbeta=3 then the area of the parallelogram for which vecalpha and vecbeta are adjacent sides is (A) sqrt(17)/2 (B) sqrt(14)/2 (C) sqrt(7)/2 (D) sqrt(241)

If |veca.vecb|=sqrt(3)|vecaxxvecb| then the angle between veca and vecb is (A) pi/6 (B) pi/4 (C) pi/3 (D) pi/2

If |veca.vecb|=sqrt(3)|vecaxxvecb| then the angle between veca and vecb is (A) pi/6 (B) pi/4 (C) pi/3 (D) pi/2

Let veca,vecb,vecc be three vectors such that |veca|=|vecb|=|vecc|=4 and angle between veca and vecb is pi/3 angle between vecb and vecc is pi/3 and angle between vecc and veca is pi/3 . The heighat of the parallelopiped whose adjacent edges are represented by the ectors veca,vecb and vecc is (A) 4sqrt(2/3) (B) 3sqrt(2/3) (C) 4sqrt(3/2) (D) 3sqrt(3/2)