" 7."a-[2b-{3a-(2b-3c)}]

|{:(-a(b^2+c^2-a^2)," "2b^3," "2c^3),(" "2a^3,-b(c^2+a^2-b^2)," "2c^3),(" "2a^3," "2b^3,-c(a^2+b^2-c^2)):}|=abc(a^2+b^2+c^2)^3

Simplify the following:(a-2b+5c) (a-b)-(a-b-c) (2a + 3c) + (6a + b) (2c-3a-5b)

Prove that a^3-(2a-b-c)^3+(b-2c)^3-(2b-c-a)^3=3(b+c-a)(a+b-2c)(2a-2b-c)

Prove that (a-2b)^3+(2b-c)^3+(c-a)^3 =3(a-2b)(2b-c)(c-a)

If a,b and c are non-coplanar vectors, prove that 3a-7b-4c, 3a-2b+c and a+b+2c are coplanar.

If a,b and c are non-coplanar vectors, prove that 3a-7b-4c, 3a-2b+c and a+b+2c are complanar.

If a,b and c are non-coplanar vectors, prove that 3a-7b-4c, 3a-2b+c and a+b+2c are coplanar.

If a,b and c are non-coplanar vectors, prove that 3a-7b-4c, 3a-2b+c and a+b+2c are coplanar.

If a,b and c are non-coplanar vectors, prove that 3a-7b-4c, 3a-2b+c and a+b+2c are coplanar.

If a,b,c are three non-coplanar vectors, then 3a-7b-4c,3a-2b+c and a+b+lamdac will be coplanar, if lamda is