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If ∣ ∣ → a × → B ∣ ∣ = 4 , ∣ ∣ → a ⋅ → B ∣ ∣ = 2 , Then | → a | 2 ∣ ∣ → B ∣ ∣ 2 = - Mathematics

MCQ

If \[\left| \vec{a} \times \vec{b} \right| = 4, \left| \vec{a} \cdot \vec{b} \right| = 2, \text{ then }  \left| \vec{a} \right|^2 \left| \vec{b} \right|^2 =\]

Options

  • 6

  • 2

  • 20

  • 8

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Solution

\[\text{ We know } \]

\[ \left( \vec{a} . \vec{b} \right)^2 + \left| \vec{a} \times \vec{b} \right|^2 = \left| \vec{a} \right|^2 \left| \vec{b} \right|^2 . . . (1)\]

\[\left| \vec{a} . \vec{b} \right| = 2 (\text{ Given } )\]

\[ \Rightarrow \left| \vec{a} . \vec{b} \right|^2 = \left( \vec{a} . \vec{b} \right)^2 \]

\[\text{ From (1), we get } \]

\[ \left( 2 \right)^2 + \left( 4 \right)^2 = \left| \vec{a} \right|^2 \left| \vec{b} \right|^2 \]

\[ \Rightarrow \left| \vec{a} \right|^2 \left| \vec{b} \right|^2 = 20\]

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APPEARS IN

RD Sharma Class 12 Maths
Chapter 25 Vector or Cross Product
MCQ | Q 12 | Page 35
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