Let a- -2- - -2k- -b- - - If c- is a vector such that a- -c- - c- and - c- -a- -2- 2 and angle between a-b- and c- is 30o- Then- - a-b- -c- equals

The correct option is C 3 2 We have ⇒a⃗ .c⃗ = | c⃗ #160; | #160; and | c⃗ a⃗ #160; | =2√( 2 ) ⇒ | c⃗ a⃗| =| c⃗ #160; | #160 ...

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Byju's Answer

Standard XII

Mathematics

Modulus of a Complex Number

Let a⃗ =2î ...

Question

Let $\to a = 2^i +^j - 2^k, \to b =^i +^j$ . If $\to c$ is a vector such that $\to a . \to c = | \to c |$ and $| \to c - \to a | = 2 \sqrt{2}$ and angle between $\to a \times \to b$ and $\to c$ is $30^{o}$ . Then, $∣ ∣ (\to a \times \to b) \times \to c ∣ ∣$ equals

\frac{3}{2}

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\frac{2}{3}

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2

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

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Solution

The correct option is C $\frac{3}{2}$
We have $\Rightarrow \to a . \to c = | \to c |$ and $| \to c - \to a | = 2 \sqrt{2}$

$\Rightarrow | \to c - \to a | = {| \to c |}^{2} + {| \to a |}^{2} - 2 \to a . \to c = 8$

$\Rightarrow {| \to c |}^{2} + 9 - 2 | \to c | = 8 \Rightarrow {(| \to c | - 1)}^{2} = 0 \Rightarrow | \to c | = 1$

Now

$∣ ∣ (\to a \times \to b) \times \to c ∣ ∣ = ∣ ∣ \to a \times \to b ∣ ∣ . | \to c | sin 30^{o}$
$= \frac{1}{2} ∣ ∣ \to a \times \to b ∣ ∣ = \frac{1}{2} \times 3 = \frac{3}{2}$ ..... $⎡ ⎢ ⎣ ∵ ∣ ∣ \to a \times \to b ∣ ∣ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 2 & 1 & - 2 1 & 1 & 0 \end{matrix} ∣ ∣ ∣ ∣ ∣ = 2^i - 2^j +^k ⎤ ⎥ ⎦$

$∴ ∣ ∣ (\to a \times \to b) \times \to c ∣ ∣ = \frac{3}{2}$

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Similar questions

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Let →a=2^i+^j−2^k,→b=^i+^j. If →c is a vector such that →a.→c=|→c| and |→c−→a|=2√2 and angle between →a×→b and →c is 30o. Then, ∣∣(→a×→b)×→c∣∣ equals

Let $\to a = 2^i +^j - 2^k, \to b =^i +^j$ . If $\to c$ is a vector such that $\to a . \to c = | \to c |$ and $| \to c - \to a | = 2 \sqrt{2}$ and angle between $\to a \times \to b$ and $\to c$ is $30^{o}$ . Then, $∣ ∣ (\to a \times \to b) \times \to c ∣ ∣$ equals