Question

of
la1 = 3 1b1 = 4 and a. b =9, then
find la xbl​

Answer 1

GIVEN :–

$\\ \bf \implies | \overrightarrow{a}| = 3 \: , \:| \overrightarrow{b}| =4\: , \: \overrightarrow{a}.\overrightarrow{b} = 9$

TO FIND :–

• Value of $\bf \overrightarrow{a} \times \overrightarrow{b} =?$

SOLUTION :–

$\\ \bf \implies\overrightarrow{a}.\overrightarrow{b} = 9$

$\\ \bf \implies | \overrightarrow{a}| | \overrightarrow{b}| \cos( \theta) = 9$

$\\ \bf \implies (3)(4)\cos( \theta) = 9$

$\\ \bf \implies \cos( \theta) = \dfrac{9}{12}$

$\\ \bf \implies \cos(\theta) = \dfrac{3}{4}$

• We should write this as –

$\\ \bf \implies \sqrt{1 - { \sin}^{2}(\theta)} = \dfrac{3}{4}$

• Square on both side –

$\\ \bf \implies 1 - { \sin}^{2}(\theta)= \dfrac{9}{16}$

$\\ \bf \implies { \sin}^{2}(\theta)= 1 - \dfrac{9}{16}$

$\\ \bf \implies { \sin}^{2}(\theta)= \dfrac{16 - 9}{16}$

$\\ \bf \implies { \sin}^{2}(\theta)= \dfrac{7}{16}$

$\\ \large \implies{ \boxed{ \bf\sin(\theta)= \dfrac{ \sqrt{7}}{4}}}$

• Now let's find –

$\\ \implies \bf\overrightarrow{a} \times \overrightarrow{b} =| \overrightarrow{a}| | \overrightarrow{b}| \sin(\theta)$

$\\ \implies \bf\overrightarrow{a} \times \overrightarrow{b} =(3)(4)\dfrac{ \sqrt{7}}{4}$

$\\ \large \implies \red{ \boxed{\bf\overrightarrow{a} \times \overrightarrow{b} =3\sqrt{7}}}$

Answer 2

Step-by-step explanation:

GIVEN :–

$\\ \bf \implies | \overrightarrow{a}| = 3 \: , \:| \overrightarrow{b}| =4\: , \: \overrightarrow{a}.\overrightarrow{b} = 9$

TO FIND :–

• Value of $\bf \overrightarrow{a} \times \overrightarrow{b} =?$

SOLUTION :–

$\\ \bf \implies\overrightarrow{a}.\overrightarrow{b} = 9$

$\\ \bf \implies | \overrightarrow{a}| | \overrightarrow{b}| \cos( \theta) = 9$

$\\ \bf \implies (3)(4)\cos( \theta) = 9$

$\\ \bf \implies \cos( \theta) = \dfrac{9}{12}$

$\\ \bf \implies \cos(\theta) = \dfrac{3}{4}$

• We should write this as –

$\\ \bf \implies \sqrt{1 - { \sin}^{2}(\theta)} = \dfrac{3}{4}$

• Square on both side –

$\\ \bf \implies 1 - { \sin}^{2}(\theta)= \dfrac{9}{16}$

$\\ \bf \implies { \sin}^{2}(\theta)= 1 - \dfrac{9}{16}$

$\\ \bf \implies { \sin}^{2}(\theta)= \dfrac{16 - 9}{16}$

$\\ \bf \implies { \sin}^{2}(\theta)= \dfrac{7}{16}$

$\\ \large \implies{ \boxed{ \bf\sin(\theta)= \dfrac{ \sqrt{7}}{4}}}$

• Now let's find –

$\\ \implies \bf\overrightarrow{a} \times \overrightarrow{b} =| \overrightarrow{a}| | \overrightarrow{b}| \sin(\theta)$

$\\ \implies \bf\overrightarrow{a} \times \overrightarrow{b} =(3)(4)\dfrac{ \sqrt{7}}{4}$

$\\ \large \implies \red{ \boxed{\bf\overrightarrow{a} \times \overrightarrow{b} =3\sqrt{7}}}$