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Model Paper 3 — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSModel Paper 31 Mark
Question
If the points $A (-1,3,2), B (-4,2,-2)$ and $C (5,5, \lambda)$ are collinear then the value of $\lambda$ is
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Answer

Determinant of these point should be zero
$\left|\begin{array}{ccc}-1 & 3 & 2 \\ -4 & 2 & -2 \\ 5 & 5 & \lambda\end{array}\right|=0$
$-1(2 \lambda+10)-3(-4 \lambda+10)+2(-20-10)=0$
$10 \lambda=10+30+60=100$
$\lambda=10$

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