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)=2 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 vec(a)*vec(b)=vec(b)*vec(c),vec(a)=0, then the value of [vec(a),vec(b),vec(c)] is

[vec(a)vec(b)vec(c )]=[vec(b)vec(c )vec(a)]=[vec(c )vec(a)vec(b)] .

prove that (vec(a)+vec(b)).(vec(a)+vec(b))=|vec(a)|^(2)+|vec(b)|^(2) , if and only if vec(a),vec(b) are perpendicular, given vec(a) ne vec(0), vec(b) ne vec(0) .

Prove that (vec(a)+vec(b)).(vec(a)+vec(b)) = |vec(a)|^(2) + |vec(b)|^(2) , if and only if vec(a) , vec(b) are perpendicular , given vec(a) 1= vec (0) , vec (b) != vec (0)

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

Let vec(a), vec(b), vec(c ) be such that vec(c ) ne vec(0), vec(a) xx vec(b)= vec(c ) and vec(b) xx vec(c )= vec(a) then show that vec(a), vec(b) and vec(c ) are pairwise perpendicular, |vec(b)|=1 and |vec(c )|= |vec(a)| .

If vec(a) xx vec(b) = vec(c ) xx vec(d) and vec(a) xx vec(c )= vec(b) xx vec(d) then show that vec(a)- vec(d) and vec(b) -vec(c ) are parallel vectors.

If vec (a) xx vec(b) = vec (c ) xx vec(d) and vec (a) xx vec ( c) = vec (b) xx vec (d ) , show that vec(a) - vec (d) is parallel vec(b) - vec (c) , where to vec (a) != vec (d) and vec ( b) != vec (c )