If a plane passes through the points (−1,k,0),(2,k,−1),(1,1,2) and is parallel to the line 1x−1=22y+1=−1z+1, then the value of (k−1)(k−2)k2+1 is:
Explanation
Solution
Vectors: v1=(3,0,−1), v2=(2,k−1,−2), d=(1,1,−1)
Scalar Triple Product =0⟹321amp;0amp;k−1amp;1amp;−1amp;−2amp;−1=0
k=34
Putting k=4/3 in (k−1)(k−2)k2+1⟹613
Option: (2)
Explanation
Solution
Vectors: v1=(3,0,−1), v2=(2,k−1,−2), d=(1,1,−1)
Scalar Triple Product =0⟹321amp;0amp;k−1amp;1amp;−1amp;−2amp;−1=0
k=34
Putting k=4/3 in (k−1)(k−2)k2+1⟹613
Option: (2)
