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 projection vector of vec(b) on vec(a) , a ne 0 is ((vec(a).vec(b))/(|vec(a)|^(2)))vec(a) .

If vec(a) and vec(b) are perpendicular vectors, show that : (vec(a)+vec(b))^(2)=(vec(a)-vec(b))^(2) .

The vectors vec(a) and vec(b) are perpendicular if :

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))|

The vector (vec(a)+3vec(b)) is perpendicular to (7 vec(a)-5vec(b)) and (vec(a)-4vec(b)) is perpendicular to (7vec(a)-2vec(b)) . The angle between vec(a) and vec(b) is :

The vector (vec(a)+3vec(b)) is perpendicular to (7 vec(a)-5vec(b)) and (vec(a)-4vec(b)) is perpendicular to (7vec(a)-2vec(b)) . The angle between vec(a) and vec(b) is :

The vector (vec(a)+3vec(b)) is perpendicular to (7 vec(a)-5vec(b)) and (vec(a)-4vec(b)) is perpendicular to (7vec(a)-2vec(b)) . The angle between vec(a) and vec(b) is :

Show that the vectors vec(a),vec(b) and vec( c ) coplanar if vec(a)+vec(b),vec(b)+vec( c ) and vec( c )+vec(a) are coplanar.

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