If the three vectors `V_1 = i - aj - ak, V_2 = bi - j + bk, V_3 = ci + cj - k` are linearly dependent then find the value of `(1+ a)^(-1) + (1 + b)^(-1) + (1 + c)^(-1)`

If the vectors vec r_(1) = ai+j+k, vec r_(2) = i + bj + k, vec r_(3) = i + j + ck ( a ne 1, b ne 1, c ne 1) are coplanar then the value of 1/(1-a) + 1/(1-b) + 1/(1-c) =

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 the vectors vec A = a hat i + hat j + hat k, vec B = hat i + b hat j + hat k and vec C = hat i + hat j + chat k are coplanar, then (1)/(1-a) + (1)/(1-b) +(1)/(1-c) = 1 where a,b, c ne 1 .

If the vectors ahat 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) .

Let vec V_1=3a x^2 hat i-2(x-1) hat j and vec V_2=b(x-1) hat i+x^2 hat j , where a b<0. The vector vec V_1 and vec V_2 are linearly dependent for atleast one x in (0, 1) atleast one x in (-1,0) atleast one x in (1,2) no value of x in (0, 1)

Evaluate : 1/3 int ( 1 + 2v ) / ( v^2 + v + 1 )dv

What is the condition for the vectors 2i + 3j - 4k and 3i - aj + bk to be parallel ?