First slide
Introduction to 3-D Geometry
Question

The points (5,2,4),(6,- 1,2) and (8, - 7, k) are collinear, if k is equal to

Moderate
Solution

Now,

Δxy=12521611871=12|[5(1+7)2(68)+1(42+8)]|

=12|[30+434]|=0Δyz=122411217k1=12|[2(2k)4(1+7)+1(k+14)]|=12|[42k24k+14]|=12|[3k6]|=3k+62Δzx=12451261k81=12|[4(68)5(2k)+1(166k)]|=12|[810+5k+166k]|=12|[2k]|=k+22

For collinear  =0

    02+3k+622+k+222    =0    14(3k+6)2+(k+2)2    =0    9k2+36+36k+k2+4+4k=0    10k2+40k+40=0k2+4k+4=0        (k+2)2=0k=2 

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