Let veca and vecb be two unit vectors. If the vectors vecc = hata + 2 hatb and vecd = 5 hata -4 hatb are perpendicular to each other,then the angle between hata and hatb is :

Question

Let veca and vecb be two unit vectors. If the vectors vecc = hata + 2 hatb and vecd = 5 hata -4 hatb are perpendicular to each other,then the angle between hata and hatb is : (A) (π/6) (B) (π/2) (C) (π/3) (D) (π/4)

Tardigrade Admin · Accepted Answer

vecc = hata + 2 hatb vecd = 5 hata -4 hatb vecc. vecd = 0 ⇒ ( hata+2 hatb).(5 hata -4 hatb) = 0 ⇒ 5+6 hata. hatb-8 = 0 ⇒ hata. hatb = (1/2) ⇒ θ = (π/3)

Q. Let $a an d b$ be two unit vectors. If the vectors $c = \overset{a}{^} + 2 \hat{b}$ and $d = 5 \overset{a}{^} - 4 \hat{b}$ are perpendicular to each other,then the angle between $\overset{a}{^}$ and $\hat{b}$ is :

$\frac{π}{6}$

$\frac{π}{2}$

$\frac{π}{3}$

$\frac{π}{4}$

$c = \overset{a}{^} + 2 \hat{b}$
$d = 5 \overset{a}{^} - 4 \hat{b}$
$c . d = 0$
$\Rightarrow (\overset{a}{^} + 2 \hat{b}) . (5 \overset{a}{^} - 4 \hat{b}) = 0 \Rightarrow 5 + 6 \overset{a}{^} . \hat{b} - 8 = 0$
$\Rightarrow \overset{a}{^} . \hat{b} = \frac{1}{2} \Rightarrow θ = \frac{π}{3}$

Q. Let aandb be two unit vectors. If the vectors c=a^+2b^ and d=5a^−4b^ are perpendicular to each other,then the angle between a^ and b^ is :

6π​

2π​

3π​

4π​