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.