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STD 12 - 10. vector algebra — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 10. vector algebra4 Marks
MCQ
Let $\vec a $ and $\vec b $ be two unit vectors. If the vector $\vec c=\vec a+2\vec b $ and $\vec d=5\vec a-4\vec b $ are perpendicular to each other, then the angle between $\vec a$  and $\vec b$  
  • A
    $\frac{\pi }{6}$
  • B
    $\;\frac{\pi }{2}$
  • ✓
    $\;\frac{\pi }{3}$
  • D
    $\;\frac{\pi }{4}$
✓

Answer

Correct option: C.
$\;\frac{\pi }{3}$
c
Ads $\mathrm{c}$ and $\mathrm{d}$ are perpendicular. so just take their dot product and writr

c.d $=0$ $(a+2 b) \cdot(5 a-4 b)=0$

$5^{\star} 1-4 a \cdot b+10 b \cdot a-8^{\star} 1=0$

(As a and b are unit vectors, so their dot product=1)

$6 a . b=3$

$a \cdot b=1 / 2=\cos x$

$x=60$ degree

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