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If | → a | = 10 , ∣ ∣ → B ∣ ∣ = 2 and ∣ ∣ → a × → B ∣ ∣ = 16 , Find → a . → B . - Mathematics

Short Note
\[\text{ If }  \left| \vec{a} \right| = 10, \left| \vec{b} \right| = 2 \text{ and }  \left| \vec{a} \times \vec{b} \right| = 16, \text{ find }  \vec{a} . \vec{b} .\]

 

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Solution

\[\text{ We know }  \]
\[ \left( \vec{a} . \vec{b} \right)^2 + \left| \vec{a} \times \vec{b} \right|^2 = \left| \vec{a} \right|^2 \left| \vec{b} \right|^2 \]
\[ \Rightarrow \left( \vec{a} . \vec{b} \right)^2 + \left( 16 \right)^2 = \left( 10 \right)^2 \times 2^2 ( \because \left| \vec{a} \times \vec{b} \right| = 16, \left| \vec{a} \right| = 10 \text{ and  } \left| \vec{b} \right| = 2)\]
\[ \Rightarrow \left( \vec{a} . \vec{b} \right)^2 + 256 = 400\]
\[ \Rightarrow \left( \vec{a} . \vec{b} \right)^2 = 144\]
\[ \Rightarrow \left( \vec{a} . \vec{b} \right) = \pm 12\]

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APPEARS IN

RD Sharma Class 12 Maths
Chapter 25 Vector or Cross Product
very short answers | Q 9 | Page 33
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