State whether the folowing statements are trune or false giving reason in brief :
(a) As adiidtion of vector is commutive so subtraction must also be
(b) Component of a vector is equal to their difference to itself is zero
(c) Angle between two vectors can be greater than m`180^(@)`
(d) A vector cannot be divided by a vector.

Answer

(a) False, (b) True, (c) True,(d) True

Explanation

(a) False .
Let , `vecA = x_(1)hati + y_(1) hatj and vecB=x_(2) hati + y_(2) hatj`
then, `vecA + vecB = vecB + vecA = (x_(1)+ x_(2) )hati + (y_(1) + y_(2)) hatj`
But, `vecA - vecB=(x_(1) - x_(2))hati + (y_(1) +y_(2))hatj`
and `vecB - vecA = (x_(2) - x_(1)) hati + (y_(1)-y_(2))hatj`
So, `vecA - vecB ne vecB - vecA`
(b) True . (c) True.
Because angle between two vectors is represented by the
smalller of the two angle between the vectors so, it can't be
more than `180^(@)` .
(d) Ture, Because it is underfined.