How we can find out the condition of parallel and perpendicular in vectors ? And please suggest me practise questions.!
Answers
Parallel Vectors
Two vectors A and B are parallel if and only if they are scalar multiples of one another.
A = k B , k is a constant not equal to zero.
Let A = (Ax , Ay) and B = (Bx , By)
A and B are parallel if and only if A = k B
(Ax , Ay) = k (Bx , By) = (k Ax , k By)
Ax = k Bx and Ay = k By or Ax / Bx = k and Ay / By = k
Condition under which vectors A = (Ax , Ay) and B = (Bx , By) are parallel is given by
Ax / Bx = Ay / By or Ax By = Bx Ay
Perpendicular Vectors
Two vectors A and B are perpendicular if and only if their scalar product is equal to zero.
Let A = (Ax , Ay) and B = (Bx , By)
Vectors A and B are perpendicular if and only if A·B = 0
(Ax , Ay) · (Bx , By) = Ax Bx + Ay By
Hence vectors A and B are perpendicular if and only if
Ax Bx + Ay By = 0