If a b = b c 0, then for any scalar , - Vidyadip

MCQ

If $\overline{ a } \times \overline{ b }=\overline{ b } \times \overline{ c } \neq 0$, then for any scalar $\lambda$,

A
$\overline{ a }-\overline{ b }=\lambda(\overline{ c }-\overline{ b })$
B
$\overline{ b }+\overline{ c }=\lambda \overline{ a }$
C
$\overline{ a }+\overline{ b }=\lambda \overline{ c }$
✓
$\bar{a}+\bar{c}=\lambda \bar{b}$

✓

Answer

Correct option: D.

$\bar{a}+\bar{c}=\lambda \bar{b}$

(D) Given, $\overline{ a } \times \overline{ b }=\overline{ b } \times \overline{ c }$
$\Rightarrow \overline{ a } \times \overline{ b }=-(\overline{ c } \times \overline{ b }) \\ \Rightarrow \overline{ a } \times \overline{ b }+\overline{ c } \times \overline{ b }=\overline{0} \\ \Rightarrow(\overline{ a }+\overline{ c }) \times \overline{ b }=\overline{0} \\ \Rightarrow \overline{ a }+\overline{ c }=\lambda \overline{ b }$

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