If a → = 2 , b → = 5 and a → × b → = 8 , then a → · b → is equal to:

We have, a → = 2 , b → = 5 and a → × b → = 8 Now, a → × b → = a → b → sin θ = 8 ⇒ sin θ = ± 4 5 ∴ a → · b → = a → b → cos θ = 10 . ± 3 5 = ± 6 ⇒ a → · b → = 6 .

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MathematicsVectorDot Product & Its Application ( Projection etc.)Easy2 minPYQ_2021

MathematicsEasysingle choice

If $|\vec{a}| = 2, |\vec{b}| = 5$ and $|\vec{a} \times \vec{b}| = 8,$ then $|\vec{a} \cdot \vec{b}|$ is equal to:

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Answer:

Solution:

We have, $|\vec{a}| = 2, |\vec{b}| = 5$

and $|\vec{a} \times \vec{b}| = 8$

Now, $|\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \sin θ = 8$

$\Rightarrow \sin θ = \pm \frac{4}{5}$

$∴ \vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos θ$

$= 10 . (\pm \frac{3}{5}) = \pm 6$

$\Rightarrow |\vec{a} \cdot \vec{b}| = 6 .$

Stream:JEESubject:MathematicsTopic:VectorSubtopic:Dot Product & Its Application ( Projection etc.)

⏱ 2mℹ️ Source: PYQ_2021

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