If vector ` vec a+ vec b` bisects the angle between ` vec a` and ` vec b` , then prove that `| vec a|` = `| vec b|` .

If vec a and vec b are two vectors such that vec a + vec b is perpendicular to vec a - vec b ,then prove that |vec a| = |vec b| .

If theta is the angle between the unit vectors vec a and vec b , then prove that sin (theta)/(2) = 1/2|vec a - vec b|

If vec a , vec b ,a n d vec c are three vectors such that vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b , then prove that | vec a|=| vec b|=| vec c|dot

Let vec a , vec b , vec c be three unit vectors and vec a . vec b= vec a . vec c=0. If the angel between vec b and vec c is pi/3 , then find the value of |[ vec a vec b vec c]| .

If theta is the angle between the unti vectors vec a and vec b , then proves that cos((theta)/(2)) = 1/2 |vec a + vec b| .

If theta is the angle between any two vectors vec a and vec b , then |vec a. vec b| = | vec a xx vec b| , when theta is equal to

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 , angle, between vec aa n d vec b is (2pi)/3,| vec a|=sqrt(2),| vec b|=sqrt(3)a n d| vec c|=1/(sqrt(3)) , then the angel between vec aa n d vec b is a. pi/6 b. pi/4 c. pi/3 d. pi/2

For any two vectors veca and vec b show that |vec a. vec b| le |vec a||vec b| .

If vec a , vec b , vec c ,a n d vec d are four non-coplanar unit vector such that vec d make equal angles with all the three vectors vec a , vec ba n d vec c , then prove that [ vec d vec a vec b]=[ vec d vec c vec b]=[ vec d vec c vec a]dot

If vec a , vec b ,a n d vec c are three non-coplanar non-zero vecrtors, then prove that ( vec a . vec a) vec bxx vec c+( vec a . vec b) vec cxx vec a+( vec a . vec c) vec axx vec b=[ vec b vec c vec a] vec a