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

$kb=-pb$

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

Given the vectors vec AB = 3ul a + k ul bvec AB = 3ul a + k ul b and vec BC = -5 ul a - ul bvec BC = -5 ul a - ul b. Find the value of kk if the points AA,BB and CC are collinear.?