Let a- b- c- be three vectors having magnitudes 1- 1 and 2 respectively- If a- a-c- - b- - 0- then angle between a- and c- is

The correct option is C Both A and B We know, a⃗⊥a⃗ ⃗×⃗ ⃗c⃗ ∴a⃗× (a⃗×⃗ ⃗c⃗)=|a⃗||a⃗×⃗ ⃗c⃗|n̂ |a|=1, |a× c|=1×2 cosθ=2cosθ #160; ( ...

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Standard X

Mathematics

Section Formula

Let a⃗, b⃗,...

Question

Let $\to a, \to b, \to c$ be three vectors having magnitudes $1, 1$ and $2$ respectively. If $\to a \times (\to a \times \to c) + \to b = \to 0$ , then angle between $\to a$ and $\to c$ is

\frac{π}{6}

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\frac{5 π}{6}

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\frac{π}{3}

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Both

A

and

B

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Solution

The correct option is C Both $A$ and $B$
We know, $\to a ⊥ \to a \times c$
$∴ \to a \times (\to a \times c) = | \to a | | \to a \times c |^n$
$| a | = 1, | a \times c | = 1 \times 2 cos θ = 2 cos θ$ (where $θ$ is the angle between $\to a$ and $\to c$ )
We have, $\to a \times (\to a \times c) + \to b = \to 0$
$\Rightarrow | 2 cos θ^n | = | - \to b | \Rightarrow c o s θ = \pm \frac{1}{2}$
$∴ θ = π / 6, 5 π / 6$

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Similar questions

Q. Let

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Q. Let

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Let →a,→b,→c be three vectors having magnitudes 1,1 and 2 respectively. If →a×(→a×→c)+→b=→0, then angle between →a and →c is

The correct option is C Both A and BWe know, →a⊥→a×c∴→a×(→a×c)=|→a||→a×c|^n|a|=1,|a×c|=1×2cosθ=2cosθ (where θ is the angle between →a and →c)We have, →a×(→a×c)+→b=→0⇒|2cosθ^n|=|−→b|⇒cosθ=±12∴θ=π/6,5π/6

Let $\to a, \to b, \to c$ be three vectors having magnitudes $1, 1$ and $2$ respectively. If $\to a \times (\to a \times \to c) + \to b = \to 0$ , then angle between $\to a$ and $\to c$ is