Let a -2 -2 k- b - If -is a vector such that a - c - c - a - c -2 -3 and angle between a - b and c is 30- then - a - b - c -A- 3B-C- 3 -3-2D- 3-2

The correct option is C 3√(3)/2Given a⃗=2 î+ĵ 2 k̂, b⃗=î+ĵ |a⃗|=3, given a⃗.c⃗=|c⃗| |a⃗+c⃗|=2√(3) ⇒ |a⃗+c⃗|^2=12 ⇒ |a⃗|^2+|c⃗|^2+2a⃗.c⃗=12 ⇒ 9+|c⃗|^2+2|c⃗|=12 ...

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Byju's Answer

Standard XII

Mathematics

Vector Triple Product

Let a =2 î+ĵ-...

Question

Let $\to a = 2^i +^j - 2^k, \to b =^i +^j$ . If $^c$ is a vector such that $\to a . \to c = | \to c |, | \to a + \to c | = 2 \sqrt{3}$ and angle between $\to a \times \to b$ and $\to c$ is $30^{\circ}$ , then $| (\to a \times \to b) . \to c | =$

\frac{1}{2}

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

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3

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\frac{3}{2}

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Solution

The correct option is B $\frac{3 \sqrt{3}}{2}$
Given $\to a = 2^i +^j - 2^k, \to b =^i +^j$
$| \to a | = 3, g i v e n \to a . \to c = | \to c | | \to a + \to c | = 2 \sqrt{3} \Rightarrow | \to a + \to c |^{2} = 12 \Rightarrow | \to a |^{2} + | \to c |^{2} + 2 \to a . \to c = 12$
$\Rightarrow 9 + | \to c |^{2} + 2 | \to c | = 12 \Rightarrow | \to c |^{2} + 2 | \to c | - 3 = 0 \Rightarrow | \to c | = 1$
and $| (\to a \times \to b) . \to c | = | \to a \times \to b | | \to c | c o s 30^{\circ}$
$= | \to a \times \to b | \frac{\sqrt{3}}{2} = \frac{3 \sqrt{3}}{2}$
[here $\to a \times \to b = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 2 & 1 & - 2 1 & 1 & 0 \end{matrix} ∣ ∣ ∣ ∣ ∣$
= $^i (2) -^j (2) +^k (1) = 2^i - 2^j +^k$

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Let →a=2^i+^j−2^k,→b=^i+^j. If ^cis a vector such that →a.→c=|→c|,|→a+→c|=2√3 and angle between →a×→b and →c is 30∘, then |(→a×→b).→c|=

Let $\to a = 2^i +^j - 2^k, \to b =^i +^j$ . If $^c$ is a vector such that $\to a . \to c = | \to c |, | \to a + \to c | = 2 \sqrt{3}$ and angle between $\to a \times \to b$ and $\to c$ is $30^{\circ}$ , then $| (\to a \times \to b) . \to c | =$