If a `hat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k), and hat(i)+hat(j)+c hat(k)` are coplanar vectors, then what is the value of a+b+c-abc?

If the vectors a hat(i) + hat(j) + hat(k), hat(i) + b hat(j) + hat(k) and hat(i) + hat(j) + c hat(k) (a,b ne 1) are coplanar then the value of (1)/(1-a) + (1)/(1-b) + (1)/(1-c) is equal to

If vector hat(i)+hat(j)+hat(k), hat(i)-hat(j)+hat(k) and 2hat(i)+3hat(j)+lambda hat(k) are coplanar, then lambda is equal to

If the vectors a hat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k) and hat(i)+hat(j)+chat(k)(a, b, c, !=1) are coplanar, then the value of (1)/(1-a)+(1)/(1-b)+(1)/(1-c) is equal to

Show that the vectors -hat(i) + hat(j) - hat(k), hat(i) + hat(j) + hat(k) and hat(i) + hat(k) are coplanar.

If vectors ahat(i)+hat(j)+hat(k),hat(i)+bhat(j)+hat(k),hat(i)+hat(j)+chat(k) are coplanar, then a+b+c-abc= . . . . . . . .

If four points 2hat(i) + hat(j) + hat(k), hat(i) + hat(j) - hat(k), hat(j) - hat(k) and lamda hat(j) + hat(k) are coplanar then lamda =

If the vectors ahat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k), hat(i)+hat(j)+chat(k) , where a, b, c are coplanar, then a+b+c-abc=