If a- b - c are unit vectors such that a - b - a - c -0 and b - c -3 then the value of - a - b - a - c - isA- 0B- 2C- 1D- 1-2

The correct option is C 1 a̅.b̅=a̅.c̅⇒a̅(b̅ c̅)=0 ⇒a̅⊥b̅ c̅ | a̅×b̅ a̅×c̅ |= | a̅× (b̅ c̅) |= | a̅ | | b̅ c̅ |sinπ/2= | b̅ c̅ | | b̅ c̅ |^2=|b̅|^2+|c̅|^2 2| ...

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Byju's Answer

Standard XII

Physics

Interference in Sound Waves

if a̅, b , c ...

Question

if $¯ a, ¯ b, ¯ c a r e u n i t v e c t o r s s u c h t h a t ¯ a . ¯ b = ¯ a . ¯ c = 0 a n d (¯ b, ¯ c) = \frac{π}{3} t h e n t h e v a l u e o f ∣ ∣ ¯ a \times ¯ b - ¯ a \times ¯ c ∣ ∣$ is

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Solution

The correct option is C
1

$¯ a . ¯ b = ¯ a . ¯ c \Rightarrow ¯ a (¯ b - ¯ c) = 0 \Rightarrow ¯ a ⊥ ¯ b - ¯ c ∣ ∣ ¯ a \times ¯ b - ¯ a \times ¯ c ∣ ∣ = ∣ ∣ ¯ a \times (¯ b - ¯ c) ∣ ∣ = | ¯ a | ∣ ∣ ¯ b - ¯ c ∣ ∣ s i n \frac{π}{2} = ∣ ∣ ¯ b - ¯ c ∣ ∣ {∣ ∣ ¯ b - ¯ c ∣ ∣}^{2} = | ¯ b |^{2} + | ¯ c |^{2} - 2 | ¯ b | | ¯ c | c o s \frac{π}{3} = 1$

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if ¯a,¯b,¯c are unit vectors such that ¯a.¯b=¯a.¯c=0and(¯b,¯c)=π3 then the value of∣∣¯a×¯b−¯a×¯c∣∣ is

The correct option is C 1 ¯a.¯b=¯a.¯c⇒¯a(¯b−¯c)=0⇒¯a⊥¯b−¯c∣∣¯a×¯b−¯a×¯c∣∣=∣∣¯a×(¯b−¯c)∣∣=|¯a|∣∣¯b−¯c∣∣sinπ2=∣∣¯b−¯c∣∣∣∣¯b−¯c∣∣2=|¯b|2+|¯c|2−2|¯b||¯c|cosπ3=1

if $¯ a, ¯ b, ¯ c a r e u n i t v e c t o r s s u c h t h a t ¯ a . ¯ b = ¯ a . ¯ c = 0 a n d (¯ b, ¯ c) = \frac{π}{3} t h e n t h e v a l u e o f ∣ ∣ ¯ a \times ¯ b - ¯ a \times ¯ c ∣ ∣$ is