Show that `| vec a| vec b+| vec b| vec a` is a perpendicular to `| vec a| vec b-| vec b| vec a ,` for any two non-zero vectors ` vec aa n d vec bdot`

Show that | vec a | vec b + | vec b | vec a is perpendicular to | vec a | vec b- | vec b | vec a for any two nonzero vectors vec a and vec b

Show that |vec(a)|vec(b)-|vec(b)|vec(a) , for any two non - zero vectors vec(a) and vec(b) .

For any two vectors vec a, vec b | vec a * vec b | <= | vec a || vec b |

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] =>vec d is equally inclined to veca,vecb,vecc.

Let vec a,vec b, and vec c are vectors such that |vec a|=3,|vec b|=4 and |vec c|=5, and (vec a+vec b) is perpendicular to vec c,(vec b+vec c) is perpendicular to vec a and (vec c+vec a) is perpendicular to vec b. Then find the value of |vec a+vec b+vec c|

If vec a, vec b, vec c are three mutually perpendicular vectors such that | vec a | = | vec b | = | vec c | then (vec a + vec b + vec c) * vec a =

For any two vectors vec a and vec b prove that | vec a + vec b | <= | vec a | + | vec b |

If (vec a-vec b) * (vec a + vec b) = 0, then (a) vec a and vec b are perpendicular (b) vec a and vec b are parallel (c) | vec a | = | vec b | (d) vec a = 2vec b

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=odot

vec a, vec b, vec c, dare any four vectors then (vec a xxvec b) xx (vec c xxvec d) is a vector Perpendicular to vec a, vec b, vec c, vec d