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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
Vector $\vec a + 3\vec b$ is perpendicular to $7\vec a - 5\vec b$ and $\vec a - 5\vec b$ is perpendicular to $7\vec a + 3\vec b$ . The angle between non zero vectors $\vec a$ & $\vec b$ is
  • ✓
    $\frac {\pi}{2}$
  • B
    $\frac {\pi}{3}$
  • C
    $\frac {\pi}{6}$
  • D
    data insufficient
✓

Answer

Correct option: A.
$\frac {\pi}{2}$
a
$(\vec{a}+3 \vec{b}) \cdot(7 \vec{a}-5 \vec{b})=0$

$ \Rightarrow \quad 7|\vec a{|^2} + 16\vec a \cdot \vec b - 15|\vec b{|^2} = 0$       ........$(i)$

$(\vec{a}-5 \vec{b}) \cdot(7 \vec{a}+3 \vec{b})=0$

$ \Rightarrow \quad 7|\vec a{|^2} - 32\vec a \cdot \vec b - 15|\vec b{|^2} = 0$        .......$(ii)$

$\left( {\rm{i}} \right) - ({\rm{ii) }} \Rightarrow 48\vec a \cdot \vec b = 0\quad {\rm{ or }}\quad \vec a \bot \vec b$

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