The area of the parallelogram with vertices A (1,2,3), B (1,3, a ) , C(3,8,6) and D(3,7,3) is 265 sq. units, then a=

Step-by-step solution

Refer figure gathered A ( ABC )= A ( ABCD ) 2 = 265 2 gathered Also A ( ABC )= 1 2 | BA BC | Here BA =- j +(3- a ) k and BC =2 i +5 j +(6- a ) k aligned & Now B A B C = | array ccc i & j & k 0 & -1 & (3-a) 2 & 5 & (6-a) array | & = i (-6+a-15+5 a)- j (-6+2 a)+ k (2) & =(6 a-21) i -(2 a-6) j +2 k aligned Magnitude of BA BC = (6 a -21)^2+(2 a -6)^2+4 aligned & 1 2 (6 a-21)^2+(2 a-6)^2+4 = 265 2 & (6 a-21)^2+(2 a-6)^2+4=265 & 40 a^2-276 a+216=0 aligned a=6 from option given.