JEE MAIN - Mathematics (2008 - No. 14)
The non-zero vectors are $${\overrightarrow a ,\overrightarrow b }$$ and $${\overrightarrow c }$$ are related by $${\overrightarrow a = 8\overrightarrow b }$$ and $${\overrightarrow c = - 7\overrightarrow b \,\,.}$$ Then the angle between $${\overrightarrow a }$$ and $${\overrightarrow c }$$ is :
$$0$$
$${\pi \over 4}$$
$${\pi \over 2}$$
$$\pi $$
설명
Clearly $$\overrightarrow a = - {8 \over 7}\overrightarrow c $$
$$ \Rightarrow \overrightarrow a ||\overrightarrow c $$ and are opposite in direction
$$\therefore$$ Angle between $$\overrightarrow a $$ and $$\overrightarrow c $$ is $$\pi .$$
$$ \Rightarrow \overrightarrow a ||\overrightarrow c $$ and are opposite in direction
$$\therefore$$ Angle between $$\overrightarrow a $$ and $$\overrightarrow c $$ is $$\pi .$$