The sum of the distinct real values of `mu` for which the vectors `mu i+j+k`,`i+mu j+k`,`i+j+mu k` are coplanar is

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 sum of the distinct real values of mu for which the vectors, muhat(i)+hat(j)+hat(k),hat(i)+muhat(j)+hat(k),hat(i)+hat(j)+muhat(k) are co-planar is :

The value of alpha for which the vectors 2i-j+k, i+2j+alphak" and "3i-4j+5k are coplanar is

The number of distinct real values of lambda for which the vectors -lambda ^ (2) vec i + vec j + vec k, vec i-lambda ^ (2) vec j + vec k, vec i + vec j-lambda ^ ( 2) vec k are coplanar is

If vectors i + j + k,i - j+k and 2i + 3j + mk are coplanar, then m =

The number of distinct real values of lambda, for which the vectors -lambda^(2)hat i+hat j+k,hat i-lambda^(2)hat j+hat k and hat i+hat j-lambda^(2)hat k are coplanar is a.zero b.one c.two d.three

If the vectors i-j+k,2i+j-k,lambda i-j+lambda k are coplanar,then

The number of distinct real values of lambda for which the vectors - lambda^(2)bar(i)+bar(j)+bar(k),bar(i)-lambda^(2)bar(j)+bar(k) and bar(i)+bar(j)-lambda^(2)bar(k) are coplanar

The number of distinct real values of lambda , for which the vectors -lambda^(2)hat(i)+hat(j)+hat(k), hat(i)-lambda^(2)hat(j)+hat(k) and hat(i)+hat(j)-lambda^(2)hat(k) are coplanar, is