If the points A(−1,0,7),B(3,2,k),C(5,3,−2) are collinear then k=

The given points are  A(−1,0,7),B(3,2,k),C(5,3,−2)The direction ratios of ABare  proportional to  ⟨4,2,k−7⟩and the direction ratio of  AC are proportional to  ⟨6,3,−9⟩Since the pointsA,B,C  are collinear, the direction ratios of AB,ACare proportional It implies that  46=23=k−7−9Cross multiply and then simplify −18=3k−21⇒3k=3⇒k=1            Therefore,  k=1