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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
If the vector $i + j + k$ makes angles $\alpha ,\,\beta ,\,\gamma $ with vectors $i,\,j,k$ respectively, then
  • A
    $\alpha = \beta \ne \gamma $
  • B
    $\alpha = \gamma \ne \beta $
  • C
    $\beta = \gamma \ne \alpha $
  • ✓
    $\alpha = \beta = \gamma $
✓

Answer

Correct option: D.
$\alpha = \beta = \gamma $
d
(d) Angle between $i + j + k$ and $i$ is equal to

${\cos ^{ - 1}}\left\{ {\frac{{(i + j + k)\,.\,i}}{{|i + j + k|\,\,|i|}}} \right\} \Rightarrow \alpha = {\cos ^{ - 1}}\left( {\frac{1}{{\sqrt 3 }}} \right)$

Similarly angle between $i + j + k$ and $j$ is $\beta = {\cos ^{ - 1}}\left( {\frac{1}{{\sqrt 3 }}} \right)$ and between $i + j + k$ and

$k$ is $\gamma = {\cos ^{ - 1}}\left( {\frac{1}{{\sqrt 3 }}} \right)\,.$

Hence $\alpha = \beta = \gamma .$

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