The area of triangle with vertices (1,2,0),(1,0, a) and (0,3,1) is 6 sq. units, then the values of ' a ' are

Step-by-step solution

Refer figure A ( ABC )= 1 2 | BA BC | Here B A =2 j -a k BC =- i +3 j +(1-a) k Now BA BC = | array ccc i & j & k 0 & 2 & - a -1 & 3 & 1- a array | aligned & = i (2-2 a+3 a)- j (-a)+ k (2)=(a+2) i +(a) j +2 k & | B A B C |= (a+2)^2+(a)^2+(2)^2 aligned From given data, we write aligned & 6 = 1 2 2 a^2+4 a+8 & 4(6)=2 a^2+4 a+8 a^2+2 a-8 & (a+4)(a-2)=0 & a=-4,2 aligned