Question

Two vectors Ā and b are equal in magnitude each equal to 20 unit and are inclined at 60° to each other. The magnitude of difference of these two vectors is 10 unit O 20 unit O 20√3 unit 40 unit​

Answer 1

$\large \rm {\underbrace{\underline{Elucidation:-}}}$

$\sf \blue {\underline{\underline{✧Provided\: that:-}}}$

$\mapsto \tt {|Ā|=\bar{|B|}=20 units}$

$\mapsto \tt {\theta=60°}$

$\sf \pink {\underline{\underline{✧To\: determine:-}}}$

$\mapsto \tt {|Ā-\bar{B|}=?}$

$\sf \purple {\underline{\underline{✧We\: know:-}}}$

$\mapsto \tt {|Ā-\bar{B|}=\sqrt{A^{2}+B^{2}-2ABcos\theta}}$

$\mapsto \tt {|Ā-\bar{B|}=\sqrt{(20)^{2}+(20)^{2}-2(20)(20)×cos60°}}$

$\mapsto \tt {|Ā-\bar{B|}=\sqrt{400+400-800×\frac{1}{2}}}$

$\mapsto \tt {|Ā-\bar{B|}=\sqrt{400+400-{\cancel{800}}^{400}×\frac{1}{\cancel{2}}}}$

$\mapsto \tt {|Ā-\bar{B|}=\sqrt{400+400-400}}$

$\mapsto \tt {|Ā-\bar{B|}=\sqrt{400+{\cancel{400}}-{\cancel{400}}}}$

$\mapsto \tt {|Ā-\bar{B|}=\sqrt{400}}$

$\implies \tt \green {\boxed{\underline{|Ā-\bar{B|}=20units}}}$

$\sf \orange {\underline{\underline{✧Thereupon,}}}$

"Option-B", 20 units is the right answer.

$\sf \red {\underline{\underline{✧Note:}}}$ kindly swipe left to view the entered text completely.