A) \[32({{x}_{1}}^{2}+{{y}_{1}}^{2})\]
B) \[16({{x}_{1}}^{2}+{{y}_{1}}^{2})\]
C) \[4({{x}_{1}}^{2}+{{y}_{1}}^{2})\]
D) \[32({{x}_{1}}^{2}+{{y}_{1}}^{2})|{{z}_{1}}+{{z}_{2}}{{|}^{2}}\]
Correct Answer: A
Solution :
\[{{\left| {{x}_{1}}{{y}_{1}}-{{y}_{1}}{{z}_{2}} \right|}^{2}}+{{\left| {{y}_{1}}{{z}_{1}}-{{x}_{1}}{{z}_{2}} \right|}^{2}}\] \[=\,\,\,{{\left| {{x}_{1}}{{y}_{1}} \right|}^{2}}+{{\left| {{y}_{1}}{{z}_{2}} \right|}^{2}}-2\operatorname{Re}({{x}_{1}}{{y}_{1}}{{z}_{1}}{{z}_{2}})\] \[+\,\,|\,{{y}_{1}}{{z}_{1}}{{|}^{2}}+\,\,{{\left| {{x}_{1}}{{z}_{2}} \right|}^{2}}+\,\,2Re\,({{x}_{1}}{{y}_{1}}{{z}_{1}}{{z}_{2}})\] \[=x_{2}^{1}\,{{\left| {{z}_{1}} \right|}^{2}}+{{y}_{1}}^{2}{{\left| {{z}_{2}} \right|}^{2}}+{{y}_{1}}^{2}{{\left| {{z}_{1}} \right|}^{2}}+{{x}_{1}}^{2}{{\left| {{z}_{2}} \right|}^{2}}\] \[=x_{2}^{1}\,{{\left| {{z}_{1}} \right|}^{2}}+{{y}_{1}}^{2}{{\left| {{z}_{2}} \right|}^{2}}+{{y}_{1}}^{2}{{\left| {{z}_{1}} \right|}^{2}}+{{x}_{1}}^{2}{{\left| {{z}_{2}} \right|}^{2}}\] \[=\,\,2\left( {{x}_{1}}^{2}+{{y}_{1}}^{2} \right)\left( {{4}^{2}} \right)=32\left( {{x}_{1}}^{2}+{{y}_{1}}^{2} \right)\]
You need to login to perform this action.
You will be redirected in
3 sec
