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?
Answer & explanation
Correct answer: option 2
$(3\vec a+4\vec b+5\vec c)^2=0$
$9+16+25+2(12\vec a.\vec b+20\vec b.\vec c+15\vec a.\vec c)=0$
$50+24\vec a.\vec b+10(4\vec b.\vec c+3\vec a.\vec c)=0⇒\vec a.\vec b=0⇒\vec a⊥\vec b$
$3\vec a+4\vec b+5\vec c=0$
multiplying eq by dot of $\vec c$
$3\vec a.\vec c+4\vec b.\vec c=-5$