ĐGNL ĐHQG Hà Nội - Tư duy định lượng - Phương trình mặt phẳng

A.(a;b;c)           

B.(a;−b;−c)

C.(−a;−b;−c)

D.\[\left( {a; - b; - c; - d} \right)\]

A.(2;−1;1)

B.(2;0;−1)

C.(2;0;1)

D.(2;−1;0)

A.\[\vec n = k.\overrightarrow {n'} \]

B. \[\frac{a}{{a'}} \ne \frac{b}{{b'}} = \frac{c}{{c'}}\]

C. \[d \ne k.d'\]và \[d \ne k.d'\]

D. \[\frac{a}{{a'}} = \frac{b}{{b'}} = \frac{c}{{c'}}\]

A.hai mặt phẳng song song

B.hai mặt phẳng trùng nhau

C.hai mặt phẳng vuông góc       

D.A hoặc B đúng.

A. \[d\left( {M;\left( P \right)} \right) = \frac{{\left| {a{x_0} + b{y_0} + c{z_0} + d} \right|}}{{\sqrt {{a^2} + {b^2} + {c^2}} }}\]

B. \[d\left( {M;\left( P \right)} \right) = \frac{{a{x_0} + b{y_0} + c{z_0} + d}}{{\sqrt {{a^2} + {b^2} + {c^2}} }}\]

C. \[d\left( {M;\left( P \right)} \right) = \frac{{\left| {a{x_0} + b{y_0} + c{z_0} + d} \right|}}{{{a^2} + {b^2} + {c^2}}}\]

D. \[d\left( {M;\left( P \right)} \right) = \frac{{a{x_0} + b{y_0} + c{z_0} + d}}{{{a^2} + {b^2} + {c^2}}}\]

A.5     

B.\[\frac{{5\sqrt {11} }}{{11}}\]

C. \[\frac{5}{{11}}\]

D. \[ - \frac{5}{{\sqrt {11} }}\]

A.\[d\left( {M,\left( P \right)} \right) = d\left( {M,\left( Q \right)} \right)\]

B. \[d\left( {M,\left( P \right)} \right) > d\left( {M,\left( Q \right)} \right)\]

C. \[M \in \left( P \right)\]

D. \[d\left( {M,\left( P \right)} \right) = \sqrt 3 d\left( {M,\left( Q \right)} \right)\]

A.\[\cos \left( {\left( P \right),\left( Q \right)} \right) = \frac{{\left| {a.a' + b.b' + c.c'} \right|}}{{\sqrt {{a^2} + {b^2} + {c^2}} .\sqrt {{a^{\prime 2}} + {b^{\prime 2}} + {c^{\prime 2}}} }}\]

B. \[\cos \left( {\left( P \right),\left( Q \right)} \right) = \frac{{a.a' + b.b' + c.c'}}{{\sqrt {{a^2} + {b^2} + {c^2}} .\sqrt {{a^{\prime 2}} + {b^{\prime 2}} + {c^{\prime 2}}} }}\]

C. \[\cos \left( {\left( P \right),\left( Q \right)} \right) = \frac{{a.a' + b.b' + c.c'}}{{\sqrt {a + b + c} .\sqrt {a' + b' + c'} }}\]

D. \[\cos \left( {\left( P \right),\left( Q \right)} \right) = \frac{{\left| {a.a' + b.b' + c.c'} \right|}}{{{{\sqrt {a + b + c} }^2}.{{\sqrt {a' + b' + c'} }^2}}}\]

A.\[\alpha = \beta \]

B. \[\alpha = {180^0} - \beta \]

C. \[\sin \alpha = \sin \beta \]

D. \[\cos \alpha = \cos \beta \]

A.M(2;−1;1)

B.N(0;1;−2)

C.P(1;−2;0)

D.Q(1;−3;−4)

A.z=0

B.x+y+z=0

C.y=0

D.x=0

A.\[\left( {{P_4}} \right):\,\,2x + 3z + 1 = 0\]

B. \[\left( {{P_3}} \right):\,\,2x + 3y - z = 0\]

C. \[\left( {{P_1}} \right):\,\,2x + 3y + 1 = 0\]

D. \[\left( {{P_2}} \right):\,\,2x + 2y + 2z + 1 = 0\]

A.\({60^ \circ }\)

B. \({90^ \circ }\)

C. \({30^ \circ }\)

D. \({120^ \circ }\)