Answer the following as true or false:
(i) a and -a are collinear.
(ii) Two collinear vectors are always equal in magnitude.
(iii) Two vectors having same magnitude are collinear.
(iv) Two collinear vectors having the same magnitude are equal.
Answer the following as true or false:
(i) a and -a are collinear.
(ii) Two collinear vectors are always equal in magnitude.
(iii) Two vectors having same magnitude are collinear.
(iv) Two collinear vectors having the same magnitude are equal.
(i) True.Vectors a and -a are parallel to the same line and hence collinear.
(ii) False. Collinear vectors are those vectors that are parallel to the same line but they need not to be equal in magnitude.
(iii) False. It is not necessary for two vectors having the same magnitude to be parallel to the same line.
(iv) False. Two vectors are said to be equal, if they have the same magnitude and direction, regardless or the position of their initial points. Hence, two collinear vectors having the same magnitude need not be equal.
(i) True.Vectors a and -a are parallel to the same line and hence collinear.
(ii) False. Collinear vectors are those vectors that are parallel to the same line but they need not to be equal in magnitude.
(iii) False. It is not necessary for two vectors having the same magnitude to be parallel to the same line.
(iv) False. Two vectors are said to be equal, if they have the same magnitude and direction, regardless or the position of their initial points. Hence, two collinear vectors having the same magnitude need not be equal.
and
are
collinear.