If ` vec ra n d vec s` are non-zero constant vectors and the scalar `b` is chosen such that `| vec r+b vec s|` is minimum, then the value of `|b vec s|^2+| vec r+b vec s|^2` is equal to a.`2| vec r|^2` b. `| vec r|^2//2` c. `3| vec r""|^2` d. `|r|^2`

If vec a and vec b are two vectors such that | vec axx vec b|=2, then find the value of [ vec a vec b vec axx vec b].

If vec a and vec b are two non -zero vectors, then (vec a + vec b) .(vec a - vec b) is equal to

If vec a and vec b are non - zero vectors and |vec a+ vec b| = |vec a - vec b| , then the angle between vec a and vec b is

The value of |vec(a)+vec(b)|^(2)+|vec(a)-vec(b)|^(2) is

If vec a and vec b are two non- zero vectors such that | vec a + vec b| = |vec a - vec b| , then show that vec a and vec b are perpendicular.

If vec a , vec ba n d vec c are three non-zero vectors, no two of which ar collinear, vec a+2 vec b is collinear with vec c and vec b+3 vec c is collinear with vec a , then find the value of | vec a+2 vec b+6 vec c|dot

If vec a , vec b ,a n d vec c are there mutually perpendicular unit vectors and vec d is a unit vector which makes equal angles with vec a , vec b ,a n d vec c , the find the value off | vec a+ vec b+ vec c+ vec d|^2dot

If vec aa n d 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 bdot

If vec a , vec ba n d vec c are unit coplanar vectors, then the scalar triple product [2 vec a- vec b2 vec b- vec c2 vec c- vec a] is a. 0 b. 1 c. -sqrt(3) d. sqrt(3)

If vec a , vec ba n d vec c are non coplanar vectors and vec axx vec c is perpendicular to vec axx( vec bxx vec c), then the value of [axx( vec bxx vec c)]xx vec c is equal to a. [ vec a vec b vec c] b. 2[ vec a vec b vec c] vec b c. vec0 d. [ vec a vec b vec c] vec a