Vector Algebra — Class 12 Maths Solution

exemplar fill FillBlank NCERT,Exemp,Q.No.39,Page.219
Question

If $|\overrightarrow {\rm{a}} \times \overrightarrow {\rm{b}} {|^2} + |\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} {|^2} = 144$ and $|\overrightarrow {\rm{a}} | = 4,$ then $|\overrightarrow {\rm{b}} |$ is equal to

Step-by-step Solution

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

$= 144 = |\overrightarrow {\rm{a}} {|^2} \cdot |\overrightarrow {\rm{b}} {|^2}$

$\Rightarrow$ $|\overrightarrow {\rm{a}} {|^2}|\overrightarrow {\rm{b}} {|^2} = 144$

$\Rightarrow$ $|\overrightarrow {\rm{b}} {|^2} = \frac{{144}}{{|\overrightarrow {\rm{a}} {|^2}}} = \frac{{144}}{{16}} = 9$

$\therefore$ $|\overrightarrow {\rm{b}} | = 3$

As we know, $|\overrightarrow {\rm{a}} \times \overrightarrow {\rm{b}} {|^2} + |\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{a}} {|^2}$

$= |\overrightarrow {\rm{a}} {|^2}|\overrightarrow {\rm{b}} {|^2}$.

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