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Definition of Vector

Let a , b a...

Question

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

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Solution

$\begin{matrix} \to a \times (\to b \times \to c) = \frac{\sqrt{3}}{2} (\to b + \to c) (\to a . \to c) \to b - (\to a . \to b) \to c = \frac{\sqrt{3}}{2} (\to b + \to c) C o m p a r i n g, \to a . \to b = \frac{- \sqrt{3}}{2} | \to a | ∣ ∣ \to b ∣ ∣ cos θ = \frac{- \sqrt{3}}{2} A n g l e b e t w e e n \to a a n d \to b i s θ = 150^{0} \end{matrix}$

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Similar questions

\to a, \to b

\to c

be three unit vectors such that

\to a \times (\to b \times \to c) = \frac{\sqrt{3}}{2} (\to b + \to c)

\to b

is not parallel to

\to c

, then the angle between

\to a

\to b

\to a, \to b

\to c

are three coplanar unit vectors such that

\to a \times (\to b \times \to c) = \frac{\to b}{2}

, then the angle between

\to b

\to c

\to a, \to b, \to c

be nonzero vectors such that

(\to a \times \to b) \times \to c = \frac{1}{3} ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ \to c ∣ ∣ \to a

θ

is the angle between

\to b

\to c

sin θ =

\to a, \to b

\to c

be three non-zero vectors such that no two of them are collinear and

(\to a \times \to b) \times \to c = \frac{1}{3} ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ \to c ∣ ∣ \to a

θ

is the angle between vectors

\to b

\to c

, then a value of

sin θ

\to a, \to b, \to c

be unit vectors such that

\to a

is perpendicular to the plane of

\to b

\to c

.If the angle between

\to b

\to c

\frac{π}{3}

∣ ∣ ∣ \to a \times \to b - \to a \times \to c ∣ ∣ ∣ =

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