If ` vec aa n d vec b` are any two unit vectors, then find the greatest positive integer in the range of `(3| vec a+ vec b|)/2+2| vec a- vec b|` .

If vec a , a n d vec b are unit vectors , then find the greatest value of | vec a+ vec b|+| vec a- vec b|dot

If vec aa n d vec b are two unit vectors and theta is the angle between them, then the unit vector along the angular bisector of vec a and vec b will be given by a. ( vec a- vec b)/(cos(theta//2)) b. ( vec a+ vec b)/(2cos(theta//2)) c. ( vec a- vec b)/(2cos(theta//2)) d. none of these

If vec aa n d vec b are any two vectors of magnitudes 1 and 2, respectively, and (1-3 vec a . vec b)^2+|2 vec a+ vec b+3( vec axx vec b)|^2=47 , then the angel between vec aa n d vec b is pi//3 b. pi-cos^(-1)(1//4) c. (2pi)/3 d. cos^(-1)(1//4)

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

If vec aa n d vec b are two vectors of magnitude 1 inclined at 120^0 , then find the angle between vec ba n d vec b- vec adot

If vec a , vec b are two non-collinear vectors, prove that the points with position vectors vec a+ vec b , vec a- vec b and vec a+lambda vec b are collinear for all real values of lambdadot

If vec a and vec b are two given vectors and k is any scalar, then find the vector vec r satisfying vec rxx vec a+k vec r= vec b .

Let vec a* vec b=0,w h e r e vec aa n d vec b are unit vectors and the unit vector vec c is inclined at an angle theta to both vec aa n d vec bdot If vec c=m vec a+n vec b+p( vec axx vec b),(m ,n , p in R), then a. -pi/4lt=thetalt=pi/4 b. pi/4lt=thetalt=(3pi)/4 c. 0lt=thetalt=pi/4 d. 0lt=thetalt=(3pi)/4

If the angel between unit vectors vec aa n d vec b60^0 , then find the value of | vec a- vec b|dot

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