Question

If ${\displaystyle \left|\overline{\text{a}}\right|}$ = 10, ${\displaystyle \left|\overline{\text{b}}\right|=2}$, then ${\displaystyle \sqrt{{|\overline{\text{a}}\times \overline{\text{b}}|}^2+{|\overline{\text{a}}\cdot \overline{\text{b}}|}^2}}$ = ?

विकल्प

• 10

• 20

• 40

• 50

Answer 1

20

Explanation:

${\displaystyle \sqrt{{|\overline{\text{a}}\times \overline{\text{b}}|}^2+{|\overline{\text{a}}\cdot \overline{\text{b}}|}^2}}$

${\displaystyle =\sqrt{{\sin }^2\theta {\left|\overline{\text{a}}\right|}^2{\left|\overline{\text{b}}\right|}^2+{\cos }^2\theta {\left|\overline{\text{a}}\right|}^2{\left|\overline{\text{b}}\right|}^2}}$

${\displaystyle =\sqrt{{\left|\overline{\text{a}}\right|}^2{\left|\overline{\text{b}}\right|}^2}}$

${\displaystyle =\left|\overline{\text{a}}\right|\left|\overline{\text{b}}\right|}$

= (10)(2) = 20