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Question Number 49468 by munnabhai455111@gmail.com last updated on 07/Dec/18

Answered by tanmay.chaudhury50@gmail.com last updated on 07/Dec/18

O(0,0,0) A(x_1 ,y_1 ,z_1 ) B(x_2 ,y_2 ,z_2 ) OA^→ =ix_1 +jy_1 +kz_1 OB^→ =ix_2 +jy_2 +kz_2 area of OAB=(1/2)∣OA^→ ×OC^→ ∣ OA^→ ×OB^→ =i(y_1 z_2 −y_2 z_1 )−i(x_1 z_2 −x_2 z_1 )+k(x_1 y_2 −x_2 y_1 ) so (1/2)∣OA^→ ×OB^→ ∣ =(1/2)(√((y_1 z_2 −y_2 z_1 )^2 +(x_1 z_2 −x_2 z_1 )^2 +(x_1 y_2 −x_2 y_1 )^2 ))

O(0,0,0)A(x1,y1,z1)B(x2,y2,z2)OA→=ix1+jy1+kz1OB→=ix2+jy2+kz2areaofOAB=12∣OA→×OC→∣OA→×OB→=i(y1z2−y2z1)−i(x1z2−x2z1)+k(x1y2−x2y1)so12∣OA→×OB→∣=12(y1z2−y2z1)2+(x1z2−x2z1)2+(x1y2−x2y1)2

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