If the vectors p=(a+1) i +a j +a k , q=a i +(a+1) j +a k and r=a i +a j +(a+1) k (a R) are coplanar, then the value of a is____

Step-by-step solution

Given, vectors are aligned & p =(a+1) i +a j +a k & q =a i +(a+1) j +a k aligned and r =a i +a j +(a+1) k [p q r]=0 aligned & | array ccc a+1 & a & a a & a+1 & a a & a & a+1 array |=0 & (a+1) [(a+1)^2-a^2 ]-a [a(a+1)-a^2 ] & +a [a^2-a(a+1) ]=0 aligned aligned & (a+1)[2 a+1]-2 a[a]=0 & 2 a^2+3 a+1-2 a^2=0 & a=- 1 3 =-0.33 aligned