Question

$a$ and $b$ are mutually perpendicular unit vectors. If $r$ is a vector satisfying $r \cdot a=0, r \cdot b=1$ and $[r \,a\, b] = 1$ then $r$ is

• A. $a \times b+b$
• B. $a+(a \times b)$
• C. $b+(a \times b)$
• D. $a \times b+a$

Answer 1

Answer: (A)

Let $r=x_{1} a+x_{2} b+x_{3}(a \times b)$
Then, $r \cdot a=x_{1}|a|^{2}, r \cdot b=x_{2}|b|^{2}$
and, $r \cdot(a \times b)=x_{3}|a \times b|^{2}$
$\Rightarrow x_{1}=0, x_{2}=1, x_{3}=1 $
$\therefore r=a \times b+b$