Let - - Y- be three unit vectors such that -y-0- If the angle between - and Y- is 30- then find - in terms of - and Y-

Given, α, β,γ be three unit vectors. ⇒ |α|=|β|=|γ|=1 α.β= α. γ=0 ⇒α is perpendicular to both β and γ. Let α= n (β×γ) Taking modulus both the sides, |α| = |n| ...

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Byju's Answer

Standard XII

Mathematics

Linear Combination of Vectors

Let α⃗, β⃗, Y...

Question

Let $\to α, \to β, \to γ$ be three unit vectors such that $\to α . \to β = \to α . \to γ = 0.$ If the angle between $\to β$ and $\to γ$ is $30^{\circ},$ then find $\to α$ in terms of $\to β$ and $\to γ$ .

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Solution

Given, $\to α, \to β, \to γ$ be three unit vectors.
$\Rightarrow | \to α | = | \to β | = | \to γ | = 1$

$\to α . \to β = \to α . \to γ = 0$
$\Rightarrow \to α$ is perpendicular to both $\to β$ and $\to γ$ .

Let $\to α = n (\to β \times \to γ)$
Taking modulus both the sides,
$| \to α | = | n | | (\to β \times \to γ) |$
$\Rightarrow 1 = | n | \times 1 \times 1 \times sin 30^{\circ}$
$\Rightarrow 1 = | n | \times \frac{1}{2}$
$\Rightarrow n = \pm 2$

$∴ \to α = \pm 2 (\to β \times \to γ)$

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Let →α,→β,→γ be three unit vectors such that →α.→β=→α.→γ=0. If the angle between →β and →γ is 30∘, then find →α in terms of →β and →γ.

Let $\to α, \to β, \to γ$ be three unit vectors such that $\to α . \to β = \to α . \to γ = 0.$ If the angle between $\to β$ and $\to γ$ is $30^{\circ},$ then find $\to α$ in terms of $\to β$ and $\to γ$ .