Math

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?

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  1. 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 they are not parallel for any other value of a
    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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