Let a - b and c be three unit vectors such that a - b - c - 3 - 2 b - c - If b is not parallel to c- then the angle between a and b is-

The correct option is C 5π/ 6 a⃗× (b⃗×c⃗ ) =√( 3 ) #160; 2 (b⃗+⃗c⃗)⃗ #160; #160; #160; #160; #160; #160; #160; #160; ...

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Byju's Answer

Standard XII

Mathematics

Integration of Irrational Algebraic Fractions - 2

Let a , b a...

Question

Let $\to a, \to b$ and $\to c$ be three unit vectors such that $\to a \times (\to b \times \to c) = \frac{\sqrt{3}}{2} (\to b + \to c)$ . If $\to b$ is not parallel to $\to c$ , then the angle between $\to a$ and $\to b$ is:

\frac{3 π}{4}

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\frac{π}{2}

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\frac{2 π}{3}

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\frac{5 π}{6}

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Solution

The correct option is C $\frac{5 π}{6}$
$\to a \times (\to b \times \to c) = \frac{\sqrt{3}}{2} (\to b + \to c)$ (1)

$\to a \times (\to b \times \to c) = (\to a . \to c) \to b - (\to a . \to b) \to c$ (2)
$(1) = (2)$

$(\to a . \to c) \to b - (\to a . \to b) \to c = \frac{\sqrt{3}}{2} (\to b + \to c)$

Equating LHS =RHS

$(\to a . \to c) = \frac{\sqrt{3}}{2}$
$(\to a . \to b) = - \frac{\sqrt{3}}{2}$
$1 \times 1 c o s θ = \frac{- \sqrt{3}}{2}$
$θ = \frac{5 π}{6}$

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Let →a,→b and →c be three unit vectors such that →a×(→b×→c)=√32(→b+→c). If →b is not parallel to →c, then the angle between →a and →b is:

The correct option is C 5π6→a×(→b×→c)=√32(→b+→c) (1)→a×(→b×→c)=(→a.→c)→b−(→a.→b)→c (2)(1)=(2)(→a.→c)→b−(→a.→b)→c=√32(→b+→c)Equating LHS =RHS(→a.→c)=√32(→a.→b)=−√321×1cosθ=−√32θ=5π6

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