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

Now,Δxy=125216−118−71=12|[5(−1+7)−2(6−8)+1(−42+8)]|=12|[30+4−34]|=0Δyz=12241−121−7k1=12|[2(2−k)−4(−1+7)+1(−k+14)]|=12|[4−2k−24−k+14]|=12|[−3k−6]|=3k+62Δzx=12451261k81=12|[4(6−8)−5(2−k)+1(16−6k)]|=12|[−8−10+5k+16−6k]|=12|[−2−k]|=k+22For 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=0⇒k2+4k+4=0⇒        (k+2)2=0⇒k=−2