Let A- B- C- be the unit vectors- Suppose that A- B- - A- C- - 0 nad the angle between B- and C- is -6 then

The correct option is B A⃗ =2 (B⃗×C⃗) A ,B ,C are unit vectors A .B #160; = A .C #160; = 0 | A || B |cos p = | A || C | cosQ where ...

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Byju's Answer

Standard XII

Mathematics

Theorems for Differentiability

Let A⃗, B⃗,...

Question

Let $\to A, \to B, \to C$ , be the unit vectors. Suppose that $\to A . \to B = \to A . \to C = 0$ nad the angle between $\to B$ and $\to C$ is $\frac{π}{6}$ then

\to A = (\to B \times \to C)

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\to A = 2 (\to B \times \to C)

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\to A = 2 (\to C \times \to B)

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| \to B \times \to C | = \frac{\sqrt{3}}{2}

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Solution

The correct option is B $\to A = 2 (\to B \times \to C)$
$\to A, \to B, \to C$ are unit vectors
$\to A . \to B = \to A . \to C = 0$
$| A | | B | cos p = | A | | C | cosQ$
where $P, Q$ are the angles between, $\to A & - \to B a n d \to A & \to C$
$\begin{matrix} \Rightarrow cos p = c o s Q = 0 \Rightarrow p = Q = \frac{π}{2} N o w, \to B \times \to C = | B | | C | sin \frac{π}{6} ˆ n = \frac{1}{2} ˆ n \end{matrix}$
where $ˆ n$ is unit vector in direction of $\to B \times \to C$
$\begin{matrix} ∴ \to A i s ∥ ˆ n o r, \to A i s a n t i ∥ ˆ n ˆ n = \pm \to A \to B \times \to C = \frac{1}{2} \pm \to A ∴ \to A = 2 \pm (\to B \times \to C) \end{matrix}$
Hence, Option $B$ is correct.

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Similar questions

Q. Let

\to a, \to b, \to c

be unit vectors such that

\to a . \to b = \to a . \to c = 0

& the angle between

\to b

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Let →A,→B,→C, be the unit vectors. Suppose that →A.→B=→A.→C=0 nad the angle between →B and →C is π6 then

Let $\to A, \to B, \to C$ , be the unit vectors. Suppose that $\to A . \to B = \to A . \to C = 0$ nad the angle between $\to B$ and $\to C$ is $\frac{π}{6}$ then