The sum of the distinct real values of `mu`, for which the vectors, `mu hati + hatj + hatk, hati + mu hatj + hatk, hati + hatj + muhatk` are coplanar, is

The vectors lamda hati + hatj + 2 hatk, hati + lamda hatj - hatk and 2 hati - hatj + lamda hatk are coplanar if :

The number of distinct real values of lamda , for which the vectors -lamda^(2)hati+hatj+hatk, hati-lamda^(2)hatj+hatk and hati+hatj-lamda^(2)hatk are coplanar, is

The number of real values of a for which the vectors hati+2hatj+hatk, ahati+hatj+2hatk and hati+2hatj+ahatk are coplanar is

The number of real values of a for which the vectors hati+2hatj+hatk, ahati+hatj+2hatk and hati+2hatj+ahatk are coplanar is

The number of distinct real values of lamda, for which the vectors : -lamda ^(2) hati+hatj+ hatk, hati - lamda ^(2) hatj+ hatk and hati + hatj- lamda ^(2) hatk are coplanar, is :

The points with position vectors alpha hati+hatj+hatk, hati-hatj-hatk, hati+2hatj-hatk, hati+hatj+betahatk are coplanar if

The points with position vectors alpha hati+hatj+hatk, hati-hatj-hatk, hati+2hatj-hatk, hati+hatj+betahatk are coplanar if