Let vec{A}=2 hat{i}-3 hat{j}+4 hat{k} and vec{B}=4 hat{i}+j+2 hat{k} then |vec{A} × vec{B}| is equa

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3-1.Vectors

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Let $\vec{A}=2 \hat{i}-3 \hat{j}+4 \hat{k}$ and $\vec{B}=4 \hat{i}+j+2 \hat{k}$ then $|\vec{A} \times \vec{B}|$ is equal to ...................

$440$

$2 \sqrt{110}$

$\sqrt{220}$

$4 \sqrt{65}$

(b)

$\vec{A}=2 \hat{\imath}-3 \hat{\jmath}+4 \hat{k}$

$\vec{B}=4 \hat{\imath}+\hat{\jmath}+2 \hat{k}$

$|\vec{A} \times \vec{B}|=$ ?

$|\vec{A} \times \vec{B}|=? \quad\left|\begin{array}{ccc}\hat{\imath} & \hat{\jmath} & \hat{k} \\ 2 & -3 & 4 \\ 4 & 1 & 2\end{array}\right|$

$=\hat{\imath}(-6-4)-\hat{\jmath}(4-16)+k(2+12)$

$=-10 \hat{\imath}+12 \hat{\jmath}+14 \hat{k}$

$|\vec{A} \times \vec{B}|=\sqrt{(-10)^2+(12)^2+(14)^2}$

$=\sqrt{\frac{100+144+196}{\sqrt{440}}}$

$=\sqrt{440}=2 \sqrt{110}$

Standard 11

Physics

easy

(AIIMS-1996)

medium

medium

easy

easy