Let a be a unit vector perpendicular to unit vectors b and c and if the angle between b and c be - then b-c is

The correct option is C sinαa |p×q| = |p| |q| sinθ, θ being the angle between #160; p #160;and #160; q. Since #160; b, c # ...

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Standard XII

Mathematics

Position of a Line W.R.T Ellipse

Let a be a ...

Question

Let $\to a$ be a unit vector perpendicular to unit vectors $\to b$ and $\to c$ and if the angle between $\to b$ and $\to c$ be $α$ then $\to b \times \to c$ is

cos α \to a

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cosec α \to a

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sin α \to a

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None of these

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Solution

The correct option is C $sin α \to a$
$∣ ∣ \to p \times \to q ∣ ∣ = ∣ ∣ \to p ∣ ∣ ∣ ∣ \to q ∣ ∣ sin θ, θ$ being the angle between $\to p$ and $\to q .$
Since $\to b, \to c$ are unit vectors, the modulus becomes $sin α .$

Now that a vector is given by modulus times the direction, we have the answer as $sin α \to a$

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Similar questions

Q. Let

\vec{a} and \vec{b}

be two unit vectors and α be the angle between them. Then,

\vec{a} + \vec{b}

is a unit vector if
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α = \frac{π}{4}

(b)

α = \frac{π}{3}

(c)

α = \frac{2 π}{3}

(d)

α = \frac{π}{2}

Q. Let

\to a, \to b

and

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\to a, \to b, \to c

be unit vectors and

α, β, γ

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Q. Let

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be three unit vectors, such that

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\vec{c}

makes angles α and β with

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respectively, then cos α + cos β =
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Q. Let

\to a, \to b

and

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Let →a be a unit vector perpendicular to unit vectors →b and →c and if the angle between →b and →c be α then →b×→c is

The correct option is C sinα→a∣∣→p×→q∣∣=∣∣→p∣∣∣∣→q∣∣sinθ,θ being the angle between →p and →q.Since →b,→c are unit vectors, the modulus becomes sinα.Now that a vector is given by modulus times the direction, we have the answer as sinα→a

Let $\to a$ be a unit vector perpendicular to unit vectors $\to b$ and $\to c$ and if the angle between $\to b$ and $\to c$ be $α$ then $\to b \times \to c$ is