Let a and b be two unit vectors. If the vector c= a+2 b and d=5 a-4 b are perpendicular to each other, then the angle between a and b

Let a and b be two unit vectors. If the vector c= a+2 b and d=5 a…

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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