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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
The angle between the vectors $(2i + 6j + 3k)$ and $(12i - 4j + 3k)$ is
  • A
    ${\cos ^{ - 1}}\left( {\frac{1}{{10}}} \right)$
  • B
    ${\cos ^{ - 1}}\left( {\frac{9}{{11}}} \right)$
  • ✓
    ${\cos ^{ - 1}}\left( {\frac{9}{{91}}} \right)$
  • D
    ${\cos ^{ - 1}}\left( {\frac{1}{9}} \right)$
✓

Answer

Correct option: C.
${\cos ^{ - 1}}\left( {\frac{9}{{91}}} \right)$
c
(c) $\theta = {\cos ^{ - 1}}\left( {\frac{{2 \times 12 + 6 \times ( - 4) + 3(3)}}{{\sqrt {{2^2} + {6^2} + {3^2}} \sqrt {{{12}^2} + {4^2} + {3^2}} }}} \right)$

$ = {\cos ^{ - 1}}\left( {\frac{9}{{7 \times 13}}} \right) = {\cos ^{ - 1}}\left( {\frac{9}{{91}}} \right)$.

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