If hata, hatb and hatc are unit vectors satisfying hata-√3 hatb+ hatc=0, then the angle between the vectors hata and hatc is

Question

If hata, hatb and hatc are unit vectors satisfying hata-√3 hatb+ hatc=0, then the angle between the vectors hata and hatc is (A) (π/6) (B) (π/4) (C) (π/3) (D) (π/2)

Tardigrade Admin · Accepted Answer

| hata+ hatc|2=|√3 hatb|2 1+1+2 cos θ=3 where θ= angle between hata and hatc ⇒ cos θ=(1/2) So, 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 $\overset{c}{^}$ is

$\frac{π}{6}$

$\frac{π}{4}$

$\frac{π}{3}$

$\frac{π}{2}$

$∣ \overset{a}{^} + \overset{c}{^} ∣^{2} = ∣ 3 \hat{b} ∣^{2}$
$1 + 1 + 2 cos θ = 3$
where $θ =$ angle between $\overset{a}{^}$ and $\overset{c}{^}$
$\Rightarrow cos θ = \frac{1}{2}$
So, $θ = \frac{π}{3}$

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

6π​

4π​

3π​

2π​