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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
Let $\vec \lambda  = x\vec a + y\vec b + z\vec c$ and $\vec \lambda .(\vec a \times \vec b + \vec b \times \vec c + \vec c \times \vec a) = 2(x + y + z)$ (where $x + y + z \neq 0)$ then $\left[ {\vec a\,\,\vec b\,\,\vec c} \right]$ is
  • A
    $\frac {1}{2}$
  • B
    $\frac {3}{2}$
  • C
    $\frac {5}{2}$
  • ✓
    $2$
✓

Answer

Correct option: D.
$2$
d
$(x \vec{a}+y \vec{b}+2 \vec{c}) \cdot(\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a})$

$=2(x+y+z)$

$(x + y + z)\left[ {\begin{array}{*{20}{l}}
{\overrightarrow a }&{\overrightarrow b }&{\overrightarrow c }
\end{array}} \right] = 2(x + y + z)$

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