Question

Match vector operations between two vectors A and B in column I with angles between the two vectors in column II :

Column-I	Column-II
$a)|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}-\overrightarrow{B}|$	e) ${45}^0$
$b)|\overrightarrow{A}\times \overrightarrow{B}|=\overrightarrow{A}.\overrightarrow{B}$	f) ${30}^0$
$c)\overrightarrow{A}.\overrightarrow{B}=\frac{AB}{2}$	g) ${90}^0$
$d)|\overrightarrow{A}\times \overrightarrow{B}|=\frac{AB}{2}$	h) ${60}^0$

• A. $a\to e;b\to g;c\to f;d\to h$
• B. $a\to g;b\to e;c\to h;d\to f$
• C. $a\to g;b\to f;c\to e;d\to h$
• D. $a\to e;b\to g;c\to h;d\to f$

Answer 1

The correct option is B $a\to g;b\to e;c\to h;d\to f$

for c) $cos\theta =0.5$

$\theta =60c\to h$

for d) $sin\theta =0.5$

$\theta =30d\to f$

And for b) $\theta$ should be 45 as for that only $sin\theta =cos\theta$

$b\to e$