If the points \( A(-1,3,2) \) , \( B(-4,2,-2) \) and \( C(5,5,\lambda) \) are collinear , then value of \( \lambda \) is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \lambda=10 \)
For collinear points, \( \overrightarrow{AC} \) is a multiple of \( \overrightarrow{AB} \).
\( \overrightarrow{AB}=(-3,-1,-4) \)
\( \overrightarrow{AC}=(6,2,\lambda-2) \)
Comparing the first two components, \( \overrightarrow{AC}=-2\,\overrightarrow{AB} \). So the third components must satisfy
\( \lambda-2=-2(-4)=8 \)
\( \lambda=10 \)