If a^, b^ & c^ are unit vectors satisfying a^-3 b^+c^=0→, then the angle between the vectors a^ and c^ is

a=b=c=1 a+c=3b a+c2=3b2⇒1+1+2×1×cos θ=3⇒cos θ=12 ⇒θ=π3

If a^, b^ & c^ are unit vectors satisfying a^-3 b^+c^=0→, then the angle between the vectors a^ and c^ is

a=b=c=1 a+c=3b a+c2=3b2⇒1+1+2×1×cos θ=3⇒cos θ=12 ⇒θ=π3

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If $\hat{a}, \hat{b} & \hat{c}$ are unit vectors satisfying $\hat{a} - \sqrt{3} \hat{b} + \hat{c} = \vec{0},$ then the angle between the vectors $\hat{a}$ and $\hat{c}$ is

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$\frac{π}{4}$

$\frac{π}{3}$

$\frac{π}{6}$

$\frac{π}{2}$

answer is B.

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Detailed Solution

$|a| = |b| = |c| = 1 a + c = \sqrt{3} b {|a + c|}^{2} = 3 {|b|}^{2} \Rightarrow 1 + 1 + 2 \times 1 \times \cos θ = 3 \Rightarrow \cos θ = \frac{1}{2} \Rightarrow θ = \frac{π}{3}$

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