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 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

(v) (1-i) ^ (2) (1 + i) - (3-4i) ^ (2)

(9v + 1) + (3v + 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) .

(V + 1) / (V (2V + 1)) dv = - (1) / (x) dx

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

If three vectors V_(1)=alphai+j+k, V_(2)=i+betaj-2k" and "V_(3)=i+j are coplanar, and V_(1)" and "V_(3) are perpendicular, then the vector V_(1) times V_(2) is:

If the vectors ai + j + k , i + bj + k and i + j + ck, where a, b, c ne1 , are coplanar, then : 1/(1-a)+1/(1-b)+1/(1-c)=…