If `abs(vec(a)+vec(b))=abs(vec(a)-vec(b))`, then show that `vec(a) and vec(b)` are perpendicular to each other.

If vec(A) is perpendicular to vec(B) , then

Statement 1: If | vec a+ vec b|=| vec a- vec b| , then vec a and vec b are perpendicular to each other. Statement 2: If the diagonal of a parallelogram are equal magnitude, then the parallelogram is a rectangle. Which of the following Statements is/are correct ?

If vec(a) and vec(b) are two vector such that |vec(a) +vec(b)| =|vec(a)| , then show that vector |2a +b| is perpendicular to vec(b) .

Prove that abs(vec(a) times vec(b))=(vec(a)*vec(b))tantheta , where theta is the angle between vec(a) and vec(b) .

If vec(a), vec(b) and vec(c) are three vectors such that vec(a) times vec(b)=vec(c) and vec(b) times vec(c)=vec(a)," prove that "vec(a), vec(b), vec(c) are mutually perpendicular and abs(vec(b))=1 and abs(vec(c))=abs(vec(a)) .

If vec a , vec b are two vectors such that | vec a+ vec b|=| vec b|, then prove that vec a+2 vec b is perpendicular to vec a .

If vec a ,\ vec b are two vectors such that | vec a+ vec b|\ =| vec b|, then prove that vec a+2 vec b is perpendicular to vec adot

If vec a ,\ vec b ,\ are two vectors such that | vec a+ vec b|=| vec a|, then prove that 2 vec a+ vec b is perpendicular to vec bdot

If vec(A),vec(B) & vec(A)+vec(B) are three non - zero vector. Such that vec(A)+vec(B) is perpendicular to vec(B) then which of one is correct :

vec(a) and vec(b) are unit vectors and angle between them is pi/k . If vec(a)+2vec(b) and 5vec(a)-4vec(b) are perpendicular to each other then find the integer value of k.