A - and B - are two vectors and - is the angle between them- if A - B -3 A - - B - the value of - isA- 60-B- 45-C- 30-D- 90-

The correct option is A 60°We know nbsp; A→×B→=A→B→sinθ A→.B→=A→B→cosθ Putting these values in given equation nbsp; A→B→sinθ=3(A→B→cosθ) sinθ=3cosθ tanθ=3 ...

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Byju's Answer

Standard XII

Mathematics

Length of Normal

A → and B → a...

Question

$\to A$ and $\to B$ are two vectors and $θ$ is the angle between them, if $(\to A \times \to B ∣ ∣ ∣ = \sqrt{3} (\to A . \to B)$ the value of $θ$ is

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Solution

The correct option is A 60 $°$
We know
$(\to A \times \to B ∣ ∣ ∣ = (\to A ∣ ∣ ∣ (\to B ∣ ∣ ∣ sin θ$
$(\to A . \to B ∣ ∣ ∣ = (\to A ∣ ∣ ∣ (\to B ∣ ∣ ∣ cos θ$
Putting these values in given equation
$(\to A ∣ ∣ ∣ (\to B ∣ ∣ ∣ sin θ = \sqrt{3} ((\to A ∣ ∣ ∣ (\to B ∣ ∣ ∣ cos θ)$
$sin θ = \sqrt{3} cos θ$
$tan θ = \sqrt{3}$
$θ = 60 °$

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Similar questions

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∣ ∣ ∣ \to a \cdot \to b ∣ ∣ ∣ = ∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣,

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(c) 60^{\circ} (d) 90^{\circ}

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and

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If $sin θ = cos θ$ , $0 ⩽ θ ⩽ 90^{\circ}$
$(a) 30^{\circ}$
$(b) 45^{\circ}$
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→Aand →B are two vectors and θ is the angle between them, if (→A×→B∣∣∣=√3(→A.→B) the value of θ is

The correct option is A 60°We know (→A×→B∣∣∣=(→A∣∣∣(→B∣∣∣sinθ (→A.→B∣∣∣=(→A∣∣∣(→B∣∣∣cosθ Putting these values in given equation (→A∣∣∣(→B∣∣∣sinθ=√3((→A∣∣∣(→B∣∣∣cosθ) sinθ=√3cosθ tanθ=√3 θ=60°

$\to A$ and $\to B$ are two vectors and $θ$ is the angle between them, if $(\to A \times \to B ∣ ∣ ∣ = \sqrt{3} (\to A . \to B)$ the value of $θ$ is