If vector ` vec x` satisfying ` vec xxx vec a+( vec xdot vec b) vec c= vec d` is given ` vec x=lambda vec a+ vec axx( vec axx( vec dxx vec c))/(( vec adot vec c)| vec a|^2)` , then find the value of `lambdadot`

If [3 vec a+7 vec b\ vec c\ vec d]=lambda[ vec a\ vec c\ vec d]+mu[ vec b\ vec c\ vec d] , then find the value of lambda+mudot

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then

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

If veca , vec b , vec c are three vectors such that veca+ vec b+ vec c= vec0 , then prove that vec axx vec b= vec bxx vec c= vec cxx vec a

For any four vectors, vec a , vec b , vec c and vec d prove that vec d.( vec axx( vec bxx( vec cxx vec d)))=( vec b. vec d)[ vec a \ vec c \ vec d] .

Let vec a , vec ba n d vec c be unit vectors, such that vec a+ vec b+ vec c= vec x , vec adot vec x=1, vec bdot vec x=3/2,| vec x|=2. Then find the angel between c and x dot

If vec axx vec b= vec cxx vec da n d vec axx vec c= vec bxx vec d , then show that vec a- vec d , is paralelto vec b- vec c

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

Given that vec adot vec b= vec adot vec c , vec axx vec b= vec axx vec c and vec a is not a zero vector. Show that vec b= vec c dot

Given the following simultaneous equation for vectors vec xa n d vec y , vec x+ vec y= vec a , vec xxx vec y= vec b , vec xdot vec a=1,t h e n vec x= dot ( vec a+( vec axx vec b))/( vec a^2) (B) ( vec a+( vec axx vec b))/(| vec a|) (C) (( vec a+( vec axx vec b)))/( vec b^2) (D) none of these