Question

if A=2i-j+k and B=i-2j-k, find A×B?​

Answer 1

• GIVEN :

$\mapsto \:\sf \overrightarrow {A}=2 \hat{i}-\hat{j}+\hat{k}$

$\mapsto \sf \: \overrightarrow{B} = \hat{i} - 2 \hat{j} - \hat{k}$

• FORMULA REQUIRED :

$\mapsto \: \: \: \sf \overrightarrow A\times \overrightarrow B = |A | \: |B | \sin \: \theta \: \: \: \hat {n}$

• SOLUTION :

$\implies\:\sf \overrightarrow{A} \times \overrightarrow{B}=(2 \hat{i}-\hat{j}+\hat{k}) \times ( \hat{i} - 2 \hat{j} - \hat{k})$

$\implies\:\sf \overrightarrow{A} \times \overrightarrow{B} = 0 - 4 \hat{k} + 2 \hat{j} + \hat{k} + 0 + \hat{i} + \hat{j} + 0$

$\implies { \underline{\boxed{\:\sf \overrightarrow{A} \times \overrightarrow{B} = \hat{i} + 3 \hat{j} - 3 \hat{k}}}}$

__________________________________________________________

HAVE A WONDERFUL DAY...