Question

If $| \mathbf { a } + \mathbf { b } | > | \mathbf { a } - \mathbf { b } |$ then the angle between a and b is

• A. Acute
• B. Obtuse
• C. $\frac { \pi } { 2 }$
• D. $\pi$

Answer 1

Answer: (A)

Acute

Answer 2

$| \mathbf { a } + \mathbf { b } | > | \mathbf { a } - \mathbf { b } |$

Squaring both sides, we get

$a ^ { 2 } + b ^ { 2 } + 2 \mathbf { a } \cdot \mathbf { b } > a ^ { 2 } + b ^ { 2 } - 2 \mathbf { a } \cdot \mathbf { b }$

⇒ ⇒ $\cos \theta > 0$. Hence $\theta < 90 ^ { \circ }$, (acute).