Q .   I f   a × b = a × c ,       a 0 ,     b c ,   s h o w   t h a t   b =   c + t a   f o r   s o m e   s c a l a r   ' t ' . G i v e n :   a   ×   b   =   a   ×   c ,   a     0 ,   b     c T o   p r o v e :   b   =   c   +   t a   f o r   s o m e   s c a l a r   ' t ' G i v e n :   a   ×   b   =   a   ×   c ,   a     0 ,   b     c T o   p r o v e :   b   =   c   +   t a   f o r   s o m e   s c a l a r   ' t '

Dear Student,

Given: a × b = a × c, a  0, b  cTo prove: b = c + ta for some scalar 't'Proof: We have: a × b = a × c a × b - a × c = 0 a × b - c = 0Since, a  0 and b  c,a × b - c = 0 implies that a and b - c are proportional.Thus, b - c = ta b = c + ta.Hence, proved.

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