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`

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 bdot Then find the value of | vec a+ vec b+ vec c| .

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

Show that the vector vec(a) is perpendicular to the vector vec(b) - (vec(a).vec(b))/(|vec(a)|^(2))vec(a)

vec rxx vec a= vec bxx vec a ; vec rxx vec b= vec axx vec b ; vec a!= vec0; vec b!= vec0; vec a!=lambda vec b ,a n d vec a is not perpendicular to vec b , then find vec r in terms of vec aa n d vec bdot

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] ; then vec d equally inclined to vec a , vec b and vec c . (a) statement 1 is true but statement 2 is false. (b) statement 2 is true but statement 1 is false. (c)both the statements are true. (d) both the statements are false.

Let vec a , vec ba n d vec c be pairwise mutually perpendicular vectors, such that | vec a|=1,| vec b|=2,| vec c|=2. Then find the length of | vec a+ vec b+ vec c |

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

If vec a is parallel to vec bxx vec c , then ( vec axx vec b) . ( vec axx vec c) is equal to a. | vec a|^2( vec b . vec c) b. | vec b|^2( vec a . vec c) c. | vec c|^2( vec a . vec b) d. none of these

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

If | vec a|+| vec b|=| vec c| and vec a+ vec b= vec c , then find the angle between vec a and vec bdot