Question

if a and b are unit vector and theata is the acute angle between them then |a-b|=​

Answer 1

$\underline{ \boxed{ \bold{ \mathfrak{ \purple{ \huge{Answer}}}}}} \\ \\ \implies\rm \: | \vec{a}| = | \vec{b}| = 1 \: unit \\ \\ \implies\rm \: \theta = angle \: between \: \vec{a} \: and \: \vec{b} \\ \\ \implies \rm \: let \: | \vec{R}| = | \vec{a} - \vec{b}| \\ \\ \therefore \: \rm \: | \vec{R}| = \sqrt{ { | \vec{a}| }^{2} + { | \vec{b}| }^{2} - 2 | \vec{a}| | \vec{b}| cos \theta} \\ \\ { \rm\tiny{ \red{ \dag \: putting \: values \: of \: | \vec{a}| \: and \: | \vec{b}| }}} \\ \\ \star \rm \: | \vec{R}| = \sqrt{ {1}^{2} + {1}^{2} - 2(1)(1)cos \theta} \\ \\ \star \rm \: | \vec{R}| = \sqrt{2(1 - cos \theta)} \\ \\ \star \rm \: | \vec{R}| = \sqrt{2(2 {sin}^{2} \frac{ \theta}{2} )} = \sqrt{4 {sin}^{2} \frac{ \theta}{2} } \\ \\ \therefore \: \underline{ \boxed{ \rm{ \bold{ \orange{ | \vec{R}| = 2sin \frac{ \theta}{2} }}}}} \: \red{ \star}$