mng giúp mình bài này với mng ơi, chi tiết càng tốt nha

Đáp án+Giải thích các bước giải:

`a)`

`ptmp(P){(Đi qua M(x_0;y_0;z_0)),(vtpt\vec{n}=(A;B;C)):}`

`<=>``{(Đi qua M(1;-2;4)),(vtpt\vec{n}=(2;3;5)):}`

`=>A(x-x_0)+B(y-y_0)+C(z-z_0)=0`

`<=>2(x-1)+3(y+2)+5(z-4)=0`

`<=>2x-2+3y+6+5z-20=0`

`<=>2x+3y+5z-16=0`

`_____________________________`

`b)`

Gọi

`\vec{u}` là `(a_1;a_2;a_3)`

`\vec{v}` là `(b_1;b_2;b_3)`

`=>(a_2.b_3-a_3.b_2;a_3.b_1-a_1.b_3;a_2.b_2-a_2.b_1)`

`<=>(2.1-1.0;1.(-3)-3.1;3.0-2.(-3))`

`<=>(2;-6;6)`

`{(Đi qua A(0;-1;2)),(vtpt\vec{n}=\[vec{u},\vec{v}]=(2;-6;6)):}`

`=>2(x-0)-6(y+1)+6(z-2)=0`

`<=>2x-6y+6+6z-12=0`

`<=>2x-6y+6z-6=0`

`_____________________________`

`c)`

Gọi

`\vec{AB}=(3;-2;0)` là `(a_1;a_2;a_3)`

`\vec{AC}=(3;0;-1)` là `(b_1;b_2;b_3)`

`=>(a_2.b_3-a_3.b_2;a_3.b_1-a_1.b_3;a_2.b_2-a_2.b_1)`

`<=>((-2).(-1)-0.0;0.3-3.(-1);3.0-(-2).3)` 

`<=>(2;3;6)`

`{(Đi qua A(-3;0;0)),(vtpt\vec{n}=\[vec{AB},\vec{AC}]=(2;3;6)):}`

`=>2(x+3)+3(y-0)+6(z-0)=0`

`<=>2x+6+3y+6z=0`

`<=>2x+3y+6z+6=0`