Question

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

विकल्प

• 6

• 2

• 20

• 8

Answer 1

\[\text{ We know } \]

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

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

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

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

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

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