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Solution :

Let `alpha=3a-7b-4c,beta=3a-2b+c` <br> and `gamma=a+b+2c` <br> also, let `alpha=x beta, y-gamma` <br> `implies3a-7b-4c=x(3a-2b+c)+y(a+b+2c)` <br> `=(3x+y)a+(-2x+y)b+(x+2y)c` <br> since, a,b and c are non-coplanar vectors. <br> therefore, `3x+y=3,-2x+y=-7` <br> and `x+2y=-4` <br> solving first two, we find that x=2 and y=-3. these values of x annd y satisfy the third equation as well. <br> so, x+2 and y=-3 is the unique solution for the above system of equation. <br> `implies alpha=2beta-3gamma` <br> Hence, the vectors `alpha,beta and gamma` are complanar, because `alpha` is uniquely written as linear combination of other two. <br> Trick for the vector `alpha,beta, gamma` to be coplanar, we must have <br> `|(3,-7,-4),(3,-2,1),(1,1,2)|=0`, which is true <br> Hence, `alpha,beta,gamma` are coplanar.