Let a-b- and c- be non-zero vectors such that a- and b- are non-collinear satisfies a-b-c-1-3-b-c-a- If - is the angle between the vectors b- and c- then sin- equals

The correct option is D 2√(2)/3 Given that, (a⃗× nbsp; b⃗)×c⃗=1/3|b⃗||c⃗|a⃗ . And θ is the angle between the vectors b⃗ and c⃗ ...

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Byju's Answer

Standard XII

Physics

Vectors and Its Types

Let a⃗,b⃗ a...

Question

Let $\to a, \to b$ and $\to c$ be non-zero vectors such that $\to a$ and $\to b$ are non-collinear & satisfies $(\to a \times \to b) \times \to c = \frac{1}{3} | \to b | | \to c | \to a$ If $θ$ is the angle between the vectors $\to b$ and $\to c$ then $sin θ$ equals

\frac{2}{3}

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\sqrt{\frac{2}{3}}

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\frac{1}{3}

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\frac{2 \sqrt{2}}{3}

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Solution

The correct option is D $\frac{2 \sqrt{2}}{3}$
Given that, $(\to a \times \to b) \times \to c = \frac{1}{3} | \to b | | \to c | \to a$ . And $θ$ is the angle between the vectors $\to b$ and $\to c$
$(\to a \times \to b) \times \to c = (\to a . \to c) \to b - (\to b . \to c) \to a = \frac{1}{3} | \to b | | \to c | \to a$
$\Rightarrow \to a . \to c = 0$ and $cos θ = \frac{- 1}{3}$
$∴ sin θ = \frac{2 \sqrt{2}}{3}$
Hence, option D.

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Let →a,→b and →c be non-zero vectors such that →a and →b are non-collinear & satisfies (→a×→b)×→c=13|→b||→c|→a If θ is the angle between the vectors →b and →c then sinθ equals

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Let $\to a, \to b$ and $\to c$ be non-zero vectors such that $\to a$ and $\to b$ are non-collinear & satisfies $(\to a \times \to b) \times \to c = \frac{1}{3} | \to b | | \to c | \to a$ If $θ$ is the angle between the vectors $\to b$ and $\to c$ then $sin θ$ equals