If |a+b|>|a-b|, then the angle between a and b is - Vidyadip

MCQ

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

✓
Acute
B
Obtuse
C
$\frac{\pi}{2}$
D
$\pi$

✓

Answer

Correct option: A.

Acute

(A) $|\overline{ a }+\overline{ b }|>|\overline{ a }-\overline{ b }|$
Squaring both sides, we get
$\overline{ a }^2+\overline{ b }^2+2 \overline{ a } \cdot \overline{ b }>\overline{ a }^2+\overline{ b }^2-2 \overline{ a } \cdot \overline{ b }$
$\begin{array}{l}\Rightarrow 4 \overline{ a } \cdot \overline{ b }>0 \\ \Rightarrow \cos \theta>0\end{array}$
Hence, $\theta<90^{\circ}$ (acute).

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