Asked by George Carl
                For the vectors 4i +aj+6k and ai +(a-1)j +3k
a.Is there any value of a for which these to vectors will be parallel?
b)Cant these two vectors ever be parallel?
            
        a.Is there any value of a for which these to vectors will be parallel?
b)Cant these two vectors ever be parallel?
Answers
                    Answered by
            Reiny
            
    a)
well, the direction must be the same if they are parallel, so
4:a:6 = a : a-1 : 3
4/a = a/(a-1) = 6/3
then 4/a = 6/3 = 2
2a = 4
a = 2
does that work for a/(a-1) = 2 ??
LS = 2/(2-1) = 2
RS = 2
yes, a = 2
b) if they are parallel if a = 2, then <b>they are not parallel for any other value of a</b>
e.g. let a = 5
the first vector is <4, 5, 6> , the 2nd is <5 , 4, 3> , clearly not parallel
 
    
well, the direction must be the same if they are parallel, so
4:a:6 = a : a-1 : 3
4/a = a/(a-1) = 6/3
then 4/a = 6/3 = 2
2a = 4
a = 2
does that work for a/(a-1) = 2 ??
LS = 2/(2-1) = 2
RS = 2
yes, a = 2
b) if they are parallel if a = 2, then <b>they are not parallel for any other value of a</b>
e.g. let a = 5
the first vector is <4, 5, 6> , the 2nd is <5 , 4, 3> , clearly not parallel
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