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

Show that the vectors |vec(a)xxvec(b)|^(2)=|(vec(a).vec(a)" "vec(a).vec(b)),(vec(a).vec(b)" "vec(b).vec(b))|

For any two vectors vec(a) and vec(b) , show that | vec (a).vec(b)| le |vec(a)||vec(b)|

Three non-zero vectors vec(a), vec(b), vec(c) are such that no two of them are collinear. If the vector (vec(a)+vec(b)) is collinear with the vector vec(c) and the vector (vec(b)+vec(c)) is collinear with vector vec(a) , then prove that (vec(a)+vec(b)+vec(c)) is a null vector.

For the vector vec(a) and vec (b) if |vec(a) + vec(b)| = |vec(a) - vec(b)| , show that vec(a) and vec (b) are perpendicular

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

If vec (a), vec(b) and vec ( c) are three vectors of magnitude 3,4 and 5 respectively such that each vector is perpendicular to the sum of the other two vectors , prove that | vec (a) + vec(b) + vec (c ) | = 5 sqrt (2)

In each of the following find a unit a vector perpendicular to both vec (a) and vec (b) vec(a) = (2,1,1) and vec(b) = (1,-1,2)

If vectors vec aa n d vec b are two adjacent sides of a parallelogram, then the vector respresenting the altitude of the parallelogram which is the perpendicular to a is a. vec b+( vec bxx vec a)/(| vec a|^2) b. ( vec adot vec b)/(| vec b|^2) c. vec b-( vec bdot vec a)/(| vec a|^2) d. ( vec axx( vec bxx vec a))/(| vec b|^2)

Let vec aa n d vec b be unit vectors that are perpendicular to each other. Then [ vec a+( vec axx vec b) vec b+( vec axx vec b) vec axx vec b] will always be equal to 1 b. 0 c. -1 d. none of these