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Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsVectors2 Marks
MCQ
If the given vectors $\left(-b c, b^2+b c, c^2+b c\right) \left( a ^2+ ac ,- ac , c ^2+ ac \right)$ and $\left( a ^2+ ab , b ^2+ ab ,- ab \right)$ are coplanar, where none of $a , b$ and c is zero, then
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Answer

Correct option: B.
$b c+c a+a b=0$
(B) Since the given vectors are coplanar,
$\therefore\left|\begin{array}{ccc}-b c & b^2+b c & c^2+b c \\ a^2+a c & -a c & c^2+a c \\ a^2+a b & b^2+a b & -a b\end{array}\right|=0$
$\Rightarrow(a b+b c+c a)^3=0 \Rightarrow a b+b c+c a=0$

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