Let a- b- c- be three units vectors such that a- b-c- -b-c-2 and the angles between a- c- and a- b- be - and - respectively- then

The correct option is D α =π4, β =3π4 We have #160; a×(b× c) =b(a.c) c(a.b) =b(cosα) c(cosβ) Comparing the coefficients, we get cos(α) ...

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Byju's Answer

Standard XII

Mathematics

Bisector of Angle between Two Vectors

Let a⃗, b⃗,...

Question

Let $\to a, \to b, \to c$ be three units vectors such that $\to a \times (\to b \times \to c) = \frac{\to b + \to c}{\sqrt{2}}$ and the angles between $\to a, \to c$ and $\to a, \to b$ be $α$ and $β$ respectively, then

α = \frac{3 π}{4}, β = \frac{π}{4}

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α = \frac{π}{4}, β = \frac{7 π}{4}

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α = \frac{π}{4}, β = \frac{3 π}{4}

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None of these

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Solution

The correct option is D $α = \frac{π}{4}, β = \frac{3 π}{4}$
We have
$a \times (b \times c)$
$= b (a . c) - c (a . b)$
$= b (cos α) - c (cos β)$

Comparing the coefficients, we get
$cos (α) = \frac{1}{\sqrt{2}}$
$α = \frac{π}{4}$ and $cos (β) = \frac{- 1}{\sqrt{2}}$
$β = \frac{3 π}{4}$

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Similar questions

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∣ ∣ \to a + \to b + \to c ∣ ∣ = 1

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Q. If

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Let →a,→b,→c be three units vectors such that →a×(→b×→c)=→b+→c√2 and the angles between →a,→c and →a,→b be α and β respectively, then

The correct option is D α=π4,β=3π4We have a×(b×c)=b(a.c)−c(a.b)=b(cosα)−c(cosβ)Comparing the coefficients, we getcos(α)=1√2α=π4 and cos(β)=−1√2β=3π4

Let $\to a, \to b, \to c$ be three units vectors such that $\to a \times (\to b \times \to c) = \frac{\to b + \to c}{\sqrt{2}}$ and the angles between $\to a, \to c$ and $\to a, \to b$ be $α$ and $β$ respectively, then

The correct option is D $α = \frac{π}{4}, β = \frac{3 π}{4}$
We have
$a \times (b \times c)$
$= b (a . c) - c (a . b)$
$= b (cos α) - c (cos β)$

Comparing the coefficients, we get
$cos (α) = \frac{1}{\sqrt{2}}$
$α = \frac{π}{4}$ and $cos (β) = \frac{- 1}{\sqrt{2}}$
$β = \frac{3 π}{4}$