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3-1.Vectors
normal
If $\vec{A}+\vec{B}+\vec{C}=0$ then $\vec{A} \times \vec{B}$ is ............
A
$\vec{C} \times \vec{B}$
B
$\vec{B} \times \vec{C}$
C
$\vec{A} \times \vec{C}$
D
Zero
Solution
(b)
$\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$
$\Rightarrow \vec{a}=-\vec{b}-\vec{c}$
$\vec{a} \times \vec{b}=(-\vec{b}-\vec{c}) \times \vec{b}=-\vec{c} \times \vec{b}$
$\vec{b} \times \vec{c}=-\vec{c} \times \vec{b}$
$\vec{c} \times \vec{a}=\vec{c} \times(-\vec{b}-\vec{c})=-\vec{c} \times \vec{b}$
$\therefore \vec{a} \times \vec{b}=\vec{b} \times \vec{c}=\vec{c} \times \vec{a}$
Standard 11
Physics
