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 , vec b , and 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| .

Column I, Column II If | vec a+ vec b|=| vec a+2 vec b| , then angel between vec aa n d vec b is, p. 90^0 If | vec a+ vec b|=| vec a-2 vec b| , then angel between vec aa n d vec b is, q. obtuse If | vec a+ vec b|=| vec a- vec b| , then angel between vec aa n d vec b is, r. 0^0 Angle between vec axx vec b and a vector perpendicular to the vector vec cxx( vec axx vec b) is, s. acute

If vec a , vec b , vec c are unit vectors such that vec a. vec b=0= vec a. vec c and the angle between vec b and vec c is pi/3, then find the value of | vec axx vec b- vec axx vec c| .

Let vec A and vec B be two non-parallel unit vectors in a plane. If (alpha vec A+ vec B) bisects the internal angle between vec A and vec B , then find the value of alphadot

If vec(a) , vec(b) and vec (c ) are three unit vectors such that vec(a).vec(b) = vec(a).vec (c )=0 and angle between vec(b) and vec (c ) is pi/6 , prove that , vec (a) = pm 2 ( vec(b) xx vec(c ))

Let the vectors vec a and vec b be such that | vec a|=3 and | vec b|=(sqrt(2))/3, then ,vec axx vec b is a unit vector, if the angel between vec a and vec b is?

If | vec a|+| vec b|=| vec c| and vec a+ vec b= vec c , then find the angle between vec a and vec bdot

Let vec a , vec b ,a n d vec c be non-coplanar vectors and let the equation vec a^' , vec b^' , vec c ' are reciprocal system of vector vec a , vec b , vec c , then prove that vec axx vec a^'+ vec bxx vec b^'+ vec cxx vec c ' is a null vector.

If non-zero vectors vec a and vec b are equally inclined to coplanar vector vec c , then vec c can be a. (| vec a|)/(| vec a|+2| vec b|)a+(| vec b|)/(| vec a|+| vec b|) vec b b. (| vec b|)/(| vec a|+| vec b|)a+(| vec a|)/(| vec a|+| vec b|) vec b c. (| vec a|)/(| vec a|+2| vec b|)a+(| vec b|)/(| vec a|+2| vec b|) vec b d. (| vec b|)/(2| vec a|+| vec b|)a+(| vec a|)/(2| vec a|+| vec b|) vec b

If vec a , vec b , and vec c be non-zero vectors such that no two are collinear or ( vec axx vec b)xx vec c=1/3| vec b|| vec c| vec adot If theta is the acute angle between vectors vec b and vecc , then find the value of sin thetadot