Question

do the question of attachment-​

Answer 1

Explanation:

26.Evaluate

$(a)\;\;{(\vec {A}. \vec {B})}^{2} + {(\vec {A} \times \vec{B})}^{2}\\\\= {|\vec{A}||\vec{B}|\cos \theta }^{2} + {|\vec{A}||\vec{B}|\sin \theta }^{2}\\\\=|\vec{A}||\vec{B}|({\sin}^{2}\theta + {\cos}^{2}\theta)\\\\=\sf{|\vec{A}||\vec{B}|}$

$(b)\;\;{(\vec {A}. \vec {B})}^{2} - {(\vec {A} \times \vec{B})}^{2}\\\\= {|\vec{A}||\vec{B}|\cos \theta }^{2} -{|\vec{A}||\vec{B}|\sin \theta }^{2}\\\\=|\vec{A}||\vec{B}|({\cos}^{2}\theta - {\sin}^{2}\theta)\\\\=\sf{|\vec{A}||\vec{B}|\cos 2\theta}$

Concept Map :-

• $\vec{a}.\vec{b} = | \vec{a} || \vec{b}| \cos( \theta)$

• $\vec{a} \times \vec{b} = | \vec{a} || \vec{b}| \sin( \theta)$

• ${ \cos }^{2} \alpha + { \sin }^{2} \alpha = 1$

• ${ \cos }^{2} \alpha - { \sin }^{2} \alpha = \cos(2 \alpha )$