The value of the expression | | 2 + ( ) 2 is……….

| | 2 + ( ) 2 = | | 2 | | 2 2 + ( ) 2 = | | 2 | | 2 ( 1 - 2 ) + ( ) 2 = | | 2 | | 2 - | | 2 | | 2 2 + ( ) 2 = | | 2 | | 2 - ( ) 2 + ( ) 2 | | 2 + ( ) 2 = | | 2 | | 2

Vector Algebra — Class 12 Maths Solution

exemplar fill FillBlank NCERT,Exemp,Q.No.38,Page.219

Question

The value of the expression $|\overrightarrow {\rm{a}} \times \overrightarrow {\rm{b}} {|^2} + {(\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} )^2}$ is……….

Step-by-step Solution

$|\overrightarrow {\rm{a}} \times \overrightarrow {\rm{b}} {|^2} + {(\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} )^2}$

$= |\overrightarrow {\rm{a}} {|^2}|\overrightarrow {\rm{b}} {|^2}{\sin ^2}\theta + {(\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} )^2}$

$= |\overrightarrow {\rm{a}} {|^2}|\overrightarrow {\rm{b}} {|^2}\left( {1 - {{\cos }^2}\theta } \right) + {(\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} )^2}$

$= |\overrightarrow {\rm{a}} {|^2}|\overrightarrow {\rm{b}} {|^2} - |\overrightarrow {\rm{a}} {|^2}|\overrightarrow {\rm{b}} {|^2}{\cos ^2}\theta + {(\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} )^2}$

$= |\overrightarrow {\rm{a}} {|^2}|\overrightarrow {\rm{b}} {|^2} - {(\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} )^2} + {(\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} )^2}$

$|\overrightarrow {\rm{a}} \times \overrightarrow {\rm{b}} {|^2} + {(\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} )^2} = |\overrightarrow {\rm{a}} {|^2}|\overrightarrow {\rm{b}} {|^2}$

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Vector Algebra. Curated by Sachin Sharma. Free for all students.