Let ` vec a and vec b` be unit vectors such that `| vec a+ vec b|=sqrt(3)` . Then find the value of `(2 vec a+5 vec b).((3 vec a+ vec b+ vec axx vec b))dot`

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

If [ vec a vec b vec c]=2, then find the value of [( vec a+2 vec b- vec c)( vec a- vec b)( vec a- vec b- vec c)]dot

If | vec a|=| vec b|=| vec a+ vec b|=1, then find the value of | vec a- vec b|dot

If | vec a|=2| vec b|=5 and | vec axx vec b|=8, then find the value of vec a . vec bdot

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 .

Let vec aa n d vec b be unit vectors that are perpendicular to each other. Then [ vec a+( vec axx vec b) vec b+( vec axx vec b) vec axx vec b] will always be equal to 1 b. 0 c. -1 d. none of these

If vec a and vec b are unit vectors such that ( vec a+ vec b).[(2 vec a+3 vec b)xx(3 vec a-2 vec b)]=0 , then angle between veca and vec b is

Let vec a , vec b , and vec c are vectors such that | vec a|=3,| vec b|=4 and | vec c|=5, and ( vec a+ vec b) is perpendicular to vec c ,( vec b+ vec c) is perpendicular to vec a and ( vec c+ vec a) is perpendicular to vec bdot Then find the value of | vec a+ vec b+ vec c| .

If vec(a) and vec(b) are two vector such that |vec(a)| = 2, |vec(b)| =3 and vec(a).vec(b) =4 , then find the value of |vec(a)- vec(b)|

Let vec a , vec b and vec c be unit vectors such that vec a+ vec b- vec c=0. If the area of triangle formed by vectors vec a and vec b is A , then what is the value of 4A^2?