Let a- b- c- be three unit vectors such that b-c-a-c-2- If a- and c- are non-parallel- then the angles which b- makes with c- and a- are respectively

The correct option is D 90° amp; 60°b×(c×a)=c2 ⇒ (b·a)c (b·c)a = c2 ⇒((b·a) 12)c = nbsp;(b·c)a nbsp; Since a and c are non parallel unit vectors the ...

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Byju's Answer

Standard XII

Physics

Vectors and Its Types

Let a⃗, b⃗, c...

Question

Let $\to a, \to b, \to c$ be three unit vectors such that $\to b \times (\to c \times \to a) = \frac{\to c}{2} .$ If $\to a$ and $\to c$ are non-parallel, then the angles which $\to b$ makes with $\to c$ and $\to a$ are respectively

30 °

60 °

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60 °

45 °

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30 °

90 °

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90 °

60 °

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Solution

The correct option is D $90 °$ & $60 °$
$\to b \times (\to c \times \to a) = \frac{\to c}{2} \Rightarrow (\to b \cdot \to a) \to c - (\to b \cdot \to c) \to a = \frac{\to c}{2} \Rightarrow ((\to b \cdot \to a) - \frac{1}{2}) \to c = (\to b \cdot \to c) \to a$

Since $\to a$ and $\to c$ are non-parallel unit vectors therefore
$\Rightarrow \to b \cdot \to c = 0 = cos 90 °$
$\Rightarrow \to a \cdot \to b = \frac{1}{2} = cos 60 °$

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Let →a,→b,→c be three unit vectors such that →b×(→c×→a)=→c2. If →a and →c are non-parallel, then the angles which →b makes with →c and→a are respectively

The correct option is D 90° & 60°→b×(→c×→a)=→c2⇒(→b⋅→a)→c−(→b⋅→c)→a=→c2⇒((→b⋅→a)−12)→c=(→b⋅→c)→a Since →a and →c are non-parallel unit vectors therefore ⇒→b⋅→c=0=cos90° ⇒→a⋅→b=12=cos60°

Let $\to a, \to b, \to c$ be three unit vectors such that $\to b \times (\to c \times \to a) = \frac{\to c}{2} .$ If $\to a$ and $\to c$ are non-parallel, then the angles which $\to b$ makes with $\to c$ and $\to a$ are respectively