Let a- and b- be two unit vectors such that -a-b-3- If c-a-2 b-3a-b- then 2-c- is equal to-

The correct option is A √(55) nbsp; nbsp;|a+b|=√(3) ⇒ |a+b|^2=3 ⇒ |a|^2+2|a| |b| cosθ+ |b|^2 nbsp;=3 ⇒cosθ =1/2⇒θ = π/3 c=a+2b+3(a×b) ⇒ |c|^2=(a+2b+3(a× ...

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Byju's Answer

Standard XII

Mathematics

Cross Product of Two Vectors

Let a⃗ and b⃗...

Question

Let $\to a$ and $\to b$ be two unit vectors such that $| \to a + \to b | = \sqrt{3} .$ If $\to c = \to a + 2 \to b + 3 (\to a \times \to b),$ then $2 | \to c |$ is equal to:

\sqrt{55}

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\sqrt{51}

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\sqrt{43}

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\sqrt{37}

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Solution

The correct option is A $\sqrt{55}$
$| \to a + \to b | = \sqrt{3}$
$\Rightarrow | \to a + \to b |^{2} = 3$
$\Rightarrow | \to a |^{2} + 2 | \to a | | \to b | cos θ + | \to b |^{2} = 3$
$\Rightarrow cos θ = \frac{1}{2} \Rightarrow θ = \frac{π}{3}$

$\to c = \to a + 2 \to b + 3 (\to a \times \to b)$
$\Rightarrow | \to c |^{2} = (\to a + 2 \to b + 3 (\to a \times \to b)) \cdot (\to a + 2 \to b + 3 (\to a \times \to b))$
$\Rightarrow | \to c |^{2} = | \to a |^{2} + 4 | \to b |^{2} + 9 | \to a \times \to b) |^{2} + 4 \to a \cdot \to b$
$\Rightarrow | \to c |^{2} = 1 + 4 + 9 {sin}^{2} \frac{π}{3} + 4 \times \frac{1}{2}$
$\Rightarrow | \to c |^{2} = \frac{55}{4}$
$\Rightarrow | \to c | = \frac{\sqrt{55}}{2}$
$∴ 2 | \to c | = \sqrt{55}$

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Let →a and →b be two unit vectors such that |→a+→b|=√3. If →c=→a+2→b+3(→a×→b), then 2|→c| is equal to:

Let $\to a$ and $\to b$ be two unit vectors such that $| \to a + \to b | = \sqrt{3} .$ If $\to c = \to a + 2 \to b + 3 (\to a \times \to b),$ then $2 | \to c |$ is equal to: