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?

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

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