JEE MAIN - Physics (2004 - No. 69)
If $$\overrightarrow A \times \overrightarrow B = \overrightarrow B \times \overrightarrow A $$, then the angle beetween A and B is
$${\pi \over 2}$$
$${\pi \over 3}$$
$$\pi $$
$${\pi \over 4}$$
설명
$$\overrightarrow A \times \overrightarrow B = \overrightarrow B \times \overrightarrow A $$
$$\overrightarrow A \times \overrightarrow B - \overrightarrow B \times \overrightarrow A = 0$$
$$ \Rightarrow \overrightarrow A \times \overrightarrow B + \overrightarrow A \times \overrightarrow B = 0$$
$$\therefore$$ $$\overrightarrow A \times \overrightarrow B = 0$$
$$ \Rightarrow AB\sin \theta = 0$$
$$\theta = $$ $$0,\pi ,\,\,$$$$2\pi $$ ........
from the given options, $$\theta = \pi $$
$$\overrightarrow A \times \overrightarrow B - \overrightarrow B \times \overrightarrow A = 0$$
$$ \Rightarrow \overrightarrow A \times \overrightarrow B + \overrightarrow A \times \overrightarrow B = 0$$
$$\therefore$$ $$\overrightarrow A \times \overrightarrow B = 0$$
$$ \Rightarrow AB\sin \theta = 0$$
$$\theta = $$ $$0,\pi ,\,\,$$$$2\pi $$ ........
from the given options, $$\theta = \pi $$