Question

If two vectors $a$ and $b$ are such that $|a|=2,|b|=3$ and $a\cdot b=4$, then $|a-b|$ is equal to

• A. $\sqrt{3}$
• B. $\sqrt{5}$
• C. $\sqrt{7}$
• D. $2\sqrt{2}$

Answer 1

Answer: (B)

We have $|a-b{|}^2=(a-b)\cdot (a-b)$
$=a\cdot a-a\cdot b-b\cdot a+b\cdot b$
$=|a{|}^2-2(a\cdot b)+|b{|}^2$
$=(2{)}^2-2(4)+(3{)}^2$
Therefore $|a-b|=\sqrt{5}$