`(vec a+ vec b).(vec a- vec b)=`

For any two vectors vec a and vec b , show that : ( vec a+ vec b)dot( vec a- vec b)=0, when | vec a|=| vec b|dot

Find | vec a| and | vec b| , if ( vec a+ vec b)dot(( vec a- vec b))=8 and |vec a|=8 | vec b|

Prove that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b) and interpret it geometrically.

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

( vec a+2 vec b- vec c)dot{( vec a- vec b)xx( vec a- vec b- vec c)} is equal to [ vec a\ vec b\ vec c] b. c. 2[ vec a\ vec b\ vec c] d. 3[ vec a\ vec b\ vec c]

If vec a_|_ vec b , then vector vec v in terms of vec aa n d vec b satisfying the equation s vec vdot vec a=0a n d vec vdot vec b=1a n d[ vec v vec a vec b]=1 is vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^2) b. vec b/(| vec b|^)+( vec axx vec b)/(| vec axx vec b|^2) c. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^) d. none of these

vec a times(vec b timesvec c) is equal to : (A) (vec a*vec b)vec c-(vec a*vec c)vec b) (B)(vec a*vec b)vec a)-(vec a*vec b)vec c (C) (vec a*vec c)vec b-(vec a*vec b)vec c (D) (vec a*vec b)vec c-(vec a*vec c)vec b

vec aa n d vec b are two unit vectors that are mutually perpendicular. A unit vector that is equally inclined to vec a , vec ba n d vec axx vec b is a. 1/(sqrt(2))( vec a+ vec b+ vec axx vec b) b. 1/2( vec axx vec b+ vec a+ vec b) c. 1/(sqrt(3))( vec a+ vec b+ vec axx vec b) d. 1/3( vec a+ vec b+ vec axx vec b)

If vec aa n d vec b are two vectors and angle between them is theta, then | vec axx vec b|^2+( vec adot vec b)^2=| vec a|^2| vec b|^2 | vec axx vec b|=( vec adot vec b),iftheta=pi//4 vec axx vec b=( vec adot vec b) hat n ,(w h e r e hat n is unit vector, ) if theta=pi//4 ( vec axx vec b)dot( vec a+ vec b)=0

For any two vectors vec aa n d vec b , show that (1+| vec a|^2)(1+| vec b|^2)={"("1+ vec a.vec b")"^2| vec a+ vec b+( vec axx vec b)|^2