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\vec{a} and \vec{b} are vectors such that \begin{vmatrix} \vec{a}\cdot \vec{a} & \vec{a}\cdot \vec{b}\\\vec{a}\cdot \vec{b} & \vec{b}\cdot \vec{b} \end{vmatrix}=16then \left | \vec{a} \times \vec{b} \right | equals

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

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\begin{vmatrix} \vec{a}\cdot \vec{a} & \vec{a}\cdot \vec{b}\\\vec{a}\cdot \vec{b} & \vec{b}\cdot \vec{b} \end{vmatrix}=16\Rightarrow \left | \vec{a} \right |^{2}\left | \vec{b} \right|^{2}-(\vec{a}\cdot \vec{b})^2=16

\Rightarrow \left | \vec{a} \times \vec{b} \right |^{2}=16\Rightarrow \left | \vec{a} \times \vec{b} \right |=4

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himanshu.meshram

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