If hata, hatb and hatc are unit vectors satisfying hata-√3 hatb+ hatc= vec0, then the angle between the vectors hata and hatb

Question

If hata, hatb and hatc are unit vectors satisfying hata-√3 hatb+ hatc= vec0, then the angle between the vectors hata and hatb (A) (π/4) (B) (π/3) (C) (π/6) (D) (π/2)

Tardigrade Admin · Accepted Answer

Let angle between hata and hatc be θ . Now, hata-√3 hatb+ hatc =0 ⇒ ( hata+ hatc)=√3 hatb ⇒ ( hata+ hatc)⋅ ( hata+ hatc)=3( hatb. hatb) ⇒ hata. hata+ hata. hatc+ hatc. hata+ hatc. hatc=3×1 ⇒ 1+2 cos θ+1=3 ⇒ cos θ =(1/2) ⇒ θ=(π/3)

Q. If $\overset{a}{^}, \hat{b}$ and $\overset{c}{^}$ are unit vectors satisfying $\overset{a}{^} - 3 \hat{b} + \overset{c}{^} = 0,$ then the angle between the vectors $\overset{a}{^}$ and $\hat{b}$

$\frac{π}{4}$

$\frac{π}{3}$

$\frac{π}{6}$

$\frac{π}{2}$

Q. If a^,b^ and c^ are unit vectors satisfying a^−3​b^+c^=0, then the angle between the vectors a^ and b^

4π​

3π​

6π​

2π​

Let angle between a^ and c^ be θ . Now, a^−3​b^+c^=0 ⇒(a^+c^)=3​b^ ⇒(a^+c^)⋅(a^+c^)=3(b^.b^) ⇒a.^a^+a^.c^+c^.a^+c^.c^=3×1 ⇒1+2cosθ+1=3 ⇒cosθ=21​⇒θ=3π​

Q. If $\overset{a}{^}, \hat{b}$ and $\overset{c}{^}$ are unit vectors satisfying $\overset{a}{^} - 3 \hat{b} + \overset{c}{^} = 0,$ then the angle between the vectors $\overset{a}{^}$ and $\hat{b}$

$\frac{π}{4}$

$\frac{π}{3}$

$\frac{π}{6}$

$\frac{π}{2}$