Let a-2-2k- and b- Let c- be a vector such that -c-a-3-a-b-c-3 and the angle between c- and a-b- be 30o- Then a- c- is equal to

The correct option is A 2 Given, α⃗=2 + 2 k̂ b⃗=r̂+y and r( a̅)=(a⃗×b̅) ×c̅)=3 . Given, angle between |a⃗×b⃗| and c⃗ is π/ ...

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Byju's Answer

Standard XII

Physics

Angular Velocity

Let a⃗=2î+ĵ...

Question

Let $\to a = 2^i +^j - 2^k$ and $\to b =^i +^j$ . Let $\to c$ be a vector such that $| \to c - \to a | = 3 | (\to a \times \to b) \times \to c | = 3$ and the angle between $\to c$ and $\to a \times \to b$ be $30^{o}$ . Then $\to a . \to c$ is equal to

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Solution

The correct option is A $2$
Given,
$\to α = 2^ı +^ȷ - 2^k$
$\to b =^r + y$
and $r (- ¯ a) = (\to a \times ¯ b) \times ¯ c) = 3 .$
Given, angle between $| \to a \times \to b |$ and $\to c$ is $π / b$ .
Given
$\Rightarrow ∴ | \to a \times \to b | \to c ∣ * \frac{1}{2} = 3 [∵ | \to a \times \to b | = | \to a | \to b ∣ sin θ]$

$\Rightarrow | \to a \times \to b | | \to c | = 6 - (i)$
$Now,$
$¯ a \times ¯ ¯ ¯ 5 = 2^ı - 2 j + k$
$| ¯ a \times \to b | = \sqrt{4 + 4 + 1} = 3$
$Then, | \to c | = 2 [from (i)]$

$Now, | \to c - \to a | = 3$
$Squaring both sides$
$| c |^{2} + | \to a |^{2} - 2 \to c - \to a = 9$
$\Rightarrow 4 + 9 - 2 \to c \cdot {\to a}^{'} = 9$
$\Rightarrow y = 2 \to c \cdot \to a$
$\Rightarrow∴ \sqrt{c} \cdot \to a = 2$

Option A

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Similar questions

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Let →a=2^i+^j−2^k and →b=^i+^j. Let →c be a vector such that |→c−→a|=3|(→a×→b)×→c|=3 and the angle between →c and →a×→b be 30o. Then →a.→c is equal to

Let $\to a = 2^i +^j - 2^k$ and $\to b =^i +^j$ . Let $\to c$ be a vector such that $| \to c - \to a | = 3 | (\to a \times \to b) \times \to c | = 3$ and the angle between $\to c$ and $\to a \times \to b$ be $30^{o}$ . Then $\to a . \to c$ is equal to