Let a- b- and c- be three unit vectors- out of which vectors b- and c- are non-parallel- If - and - are the angles which vector a- makes with vectors b- and c- respectively and a- b-c- - 1-2b- then - - - - is equal to-

The correct option is A 30^0 (a⃗. c⃗)b⃗ (a⃗. b⃗).c⃗ = 1/2b⃗ b⃗ amp; c⃗ are linearly independent #160; ∴ a⃗.c⃗ = 1/2 amp; ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

Let a⃗, b⃗ ...

Question

Let $\to a, \to b$ and $\to c$ be three unit vectors, out of which vectors $\to b$ and $\to c$ are non-parallel. If $α$ and $β$ are the angles which vector $\to a$ makes with vectors $\to b$ and $\to c$ respectively and $\to a \times (\to b \times \to c) = \frac{1}{2} \to b$ , then $| α - β |$ is equal to:

60^{0}

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30^{0}

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90^{0}

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45^{0}

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Solution

The correct option is A $30^{0}$
$(\to a . \to c) \to b - (\to a . \to b) . \to c = \frac{1}{2} \to b$
$\to b$ & $\to c$ are linearly independent
$∴ \to a . \to c = \frac{1}{2}$ & $\to a . \to b = 0$
(All given vectors are unit vectors)
$∴ α = 60^{0}$ & $β = 90^{0}$
$∴ | α - β | = 30^{0}$

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Let →a,→b and →c be three unit vectors, out of which vectors →b and →c are non-parallel. If α and β are the angles which vector →a makes with vectors →b and →c respectively and →a×(→b×→c)=12→b, then |α−β| is equal to:

The correct option is A 300(→a.→c)→b−(→a.→b).→c=12→b→b & →c are linearly independent ∴ →a.→c=12 & →a.→b=0(All given vectors are unit vectors)∴ α=600 & β=900∴ |α−β|=300

The correct option is A $30^{0}$
$(\to a . \to c) \to b - (\to a . \to b) . \to c = \frac{1}{2} \to b$
$\to b$ & $\to c$ are linearly independent
$∴ \to a . \to c = \frac{1}{2}$ & $\to a . \to b = 0$
(All given vectors are unit vectors)
$∴ α = 60^{0}$ & $β = 90^{0}$
$∴ | α - β | = 30^{0}$