If a-b-c are unit vectors - b and c are inclined to a at an angle of -6 and the angle between b and c is -3 then a-b-a-c-

The correct option is A 0 a.b=a.c=cosπ6=√(3)2 and b.c=cosπ3=12 (a×b).(a×c) =[a.a nbsp; amp; a.b nbsp; amp; a.c nbsp; b ...

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Byju's Answer

Standard XII

Physics

Addition and Subtraction in Unit Vector Notation

If a,b,c ar...

Question

If $\to a, \to b, \to c$ are unit vectors , $\to b$ and $\to c$ are inclined to $\to a$ at an angle of $\frac{π}{6}$ and the angle between $\to b$ and $\to c$ is $\frac{π}{3}$ then $(\to a \times \to b) . (\to a \times \to c) =$

0

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1

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\frac{1}{\sqrt{2}}

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\frac{- 1}{\sqrt{3}}

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Solution

The correct option is A $0$
$\to a . \to b = \to a . \to c = cos \frac{π}{6} = \frac{\sqrt{3}}{2}$ and $\to b . \to c = cos \frac{π}{3} = \frac{1}{2}$
$(\to a \times \to b) . (\to a \times \to c)$
$= ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \to a . \to a & \to a . \to b & \to a . \to c \to b . \to a & \to b . \to b & \to b . \to c \to c . \to a & \to c . \to b & \to c . \to c \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦$
$⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 1 & \frac{\sqrt{3}}{2} & \frac{\sqrt{3}}{2} \frac{\sqrt{3}}{2} & 1 & \frac{1}{2} \frac{\sqrt{3}}{2} & \frac{1}{2} & 1 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦$
$= 1 (1 - \frac{1}{4}) - \frac{\sqrt{3}}{2} (\frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{4}) + \frac{\sqrt{3}}{2} (\frac{\sqrt{3}}{4} - \frac{\sqrt{3}}{2})$
$= \frac{3}{4} - \frac{3}{8} - \frac{3}{8}$
$= \frac{3}{4} - \frac{3}{4} = 0$

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Similar questions

Q. If

\to a, \to b, \to c

are unit vectors ,

\to b

and

\to c

are inclined to

\to a

at an angle of

\frac{π}{6}

and the angle between

\to b

and

\to c

\frac{π}{3}

then

(\to a \times \to b) . (\to a \times \to c) =

Q. If

\to a, \to b, \to c

are unit vectors equally inclined to each other at an angle

\frac{π}{3}

, then

[\to b + \to c, \to c + \to a, \to a + \to b] =

Q. Let

A

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and

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are unit vectors suppose

A . B = A . C = 0

and angle between

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and

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\frac{π}{6}

then

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¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

be unit vectors. Let

¯ ¯ b

and

¯ ¯ c

are inclined to

¯ ¯ ¯ a

each at

θ

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and

¯ ¯ c

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then which is/are correct, given that

x = (¯ ¯ ¯ a \times ¯ ¯ b) . (¯ ¯ ¯ a \times ¯ ¯ c)) . y = | ¯ ¯ ¯ a \times ¯ ¯ b - ¯ ¯ ¯ a \times ¯ ¯ c |

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If →a,→b,→c are unit vectors , →b and →c are inclined to →a at an angle of π6 and the angle between →b and →c is π3 then (→a×→b).(→a×→c)=

If $\to a, \to b, \to c$ are unit vectors , $\to b$ and $\to c$ are inclined to $\to a$ at an angle of $\frac{π}{6}$ and the angle between $\to b$ and $\to c$ is $\frac{π}{3}$ then $(\to a \times \to b) . (\to a \times \to c) =$