UPSC NDA Math Model Paper 4

Given: The points (1, 3, 1), (2, - 1, k) and (0, 7, 3) are collinear
As we know that, if the points (x1,y1,z1),(x2,y2,z2) and (x3,y3,z3) be collinear then|

x1	y1	z1
x2	y2	z2
x3	y3	z3

|=0
Here, x1=1,y1=3,z1=k,x2=2,y2=−1,z2=k, x3=0,y3=7 and z3=3
⇒|

1	3	1
2	−1	k
0	7	3

|=0
⇒1×(−3−7k)−3×(6−0)+1 ×(14−0)=0
⇒−3−7k−18+14=0
⇒k=−1
Hence, option C is the correct answer.