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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