Question

For a non-zero vector $\mathbf{a}$, the set of real numbers, satisfying $|(5 - x)\mathbf{a}| < |2\mathbf{a}|$ consists of all x such that

• A. $0 < x < 3$
• B. $3 < x < 7$
• C. $- 7 < x < - 3$
• D. $- 7 < x < 3$

Answer 1

Answer: (B)

$3 < x < 7$

Answer 2

We have, $|(5 - x)\mathbf{a}| < |2\mathbf{a}|$

⇒ $|5 - x||\mathbf{a}| < 2|\mathbf{a}|$ ⇒ $|5 - x| < 2$ ⇒ $- 2 < 5 - x < 2$

⇒ $3 < x < 7$