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Let $\vec a,\vec b,\vec c$ be three unit vectors such that $3\vec a+4\vec b+5\vec c=0$. Then which of the following statements is true? |
$\vec a$ is parallel to $\vec b$ $\vec a$ is perpendicular to $\vec b$ $\vec a$ is neither parallel nor perpendicular $\vec b$ None of the above |
$\vec a$ is perpendicular to $\vec b$ |
$(3\vec a+4\vec b+5\vec c)^2=0$ $9+16+25+2(12\vec a.\vec b+20\vec b.\vec c+15\vec a.\vec c)=0$ $50+24\vec a.\vec b+10(4\vec b.\vec c+3\vec a.\vec c)=0⇒\vec a.\vec b=0⇒\vec a⊥\vec b$ $3\vec a+4\vec b=-5\vec c$ ∵ with $\vec c$; $3\vec a.\vec c+4\vec b.\vec c=-5$ |
