Given the vectors #vec AB = 3ul a + k ul b# and #vec BC = -5 ul a - ul b#. Find the value of #k# if the points #A#,#B# and #C# are collinear.?

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Answer 1 · 2018-06-30T15:43:36

The value of #k=3/5#

If the vectors #vec(AB)# and #vec(BC)# are collinear, then

#vec(AB)=pvec(BC)# where #p in RR#

#vec(AB)= <3a, kb>#

#vec(BC)= <-5a, -b>#

Therefore,

#<3a,kb > =p <-5a, -b> = <-5pa, -pb>#

So,

#3a=-5pa#, #=>#, #p=-3/5#

And

#kb=-pb#

#=>#, #k=-p=3/5#