A - b and c be three vectors having magnitudes 1-1 and 2 respectively- If a - a - c - b -0- then the acute angle between a and c isA- -3B- 5 -12C- n-6D- -4

The correct option is C π/6 a⃗× (a⃗×c⃗)+b⃗=0 |a⃗|=|b⃗|=1 and |c⃗|=2 a⃗×d⃗= b⃗⇒ (a⃗×d⃗)^2=b^2=1 or |a⃗|^2|d⃗|^2 (a⃗.d⃗)^2=1 or (a⃗×c⃗)^2 0=1 ⇒ |a|^2|c|^2 (a ...

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Byju's Answer

Standard XII

Mathematics

Addition of Vectors

a , b and c b...

Question

$\to a, \to b$ and $\to c$ be three vectors having magnitudes 1, 1 and 2 respectively. If $\to a \times (\to a \times \to c) + \to b = 0$ , then the acute angle between $\to a$ and $\to c$ is

$\frac{π}{6}$

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$\frac{π}{4}$

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$\frac{π}{3}$

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$\frac{5 π}{12}$

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Solution

The correct option is A
$\frac{π}{6}$

$\to a \times (\to a \times \to c) + \to b = 0 | \to a | = | \to b | = 1 a n d | \to c | = 2 \to a \times \to d = - \to b \Rightarrow (\to a \times \to d)^{2} = b^{2} = 1 o r | \to a |^{2} | \to d |^{2} - (\to a . \to d)^{2} = 1 o r (\to a \times \to c)^{2} - 0 = 1 \Rightarrow | a |^{2} | c |^{2} - (\to a . \to c)^{2} = 1 \Rightarrow 4 - 2 c o s^{2} θ = 1 \Rightarrow c o s^{2} θ = \frac{3}{4} \Rightarrow θ = \frac{π}{6}$

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→a,→b and →c be three vectors having magnitudes 1, 1 and 2 respectively. If →a×(→a×→c)+→b=0 , then the acute angle between →a and →c is

The correct option is A π6 →a×(→a×→c)+→b=0|→a|=|→b|=1 and |→c|=2→a×→d=−→b⇒(→a×→d)2=b2=1or |→a|2|→d|2−(→a.→d)2=1or (→a×→c)2−0=1⇒|a|2|c|2−(→a.→c)2=1⇒4−2cos2θ=1⇒cos2θ=34 ⇒θ=π6

$\to a, \to b$ and $\to c$ be three vectors having magnitudes 1, 1 and 2 respectively. If $\to a \times (\to a \times \to c) + \to b = 0$ , then the acute angle between $\to a$ and $\to c$ is