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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 $i - j + k$ and $i + 2j + k$ is
  • A
    ${\cos ^{ - 1}}\left( {\frac{1}{{\sqrt {15} }}} \right)$
  • B
    ${\cos ^{ - 1}}\left( {\frac{4}{{\sqrt {15} }}} \right)$
  • C
    ${\cos ^{ - 1}}\left( {\frac{4}{{15}}} \right)$
  • ✓
    $\frac{\pi }{2}$
✓

Answer

Correct option: D.
$\frac{\pi }{2}$
d
(d) $(i - j + k)\,.\,(i + 2j + k) = \sqrt 3 \sqrt 6 \cos \theta $

$ \Rightarrow \cos \theta = \frac{0}{{\sqrt 3 \sqrt 6 }} \Rightarrow \theta = \frac{\pi }{2}.$

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