Câu hỏi:

Công thức tính khoảng cách từ điểm A đến đường thẳng d’ đi qua điểm M’ và có VTCP $\overrightarrow{\mathrm{u}\text{'}}$ là:

A. $\mathrm{d}\left(\mathrm{A};\mathrm{d}\text{'}\right)=\frac{\left|\left[\overrightarrow{\mathrm{AM}\text{'}},\overrightarrow{\mathrm{u}\text{'}}\right]\right|}{\left|\overrightarrow{\mathrm{u}\text{'}}\right|}$

B. B. $\mathrm{d}\left(\mathrm{A};\mathrm{d}\text{'}\right)=\frac{\left|\left[\overrightarrow{\mathrm{AM}\text{'}},\overrightarrow{\mathrm{u}\text{'}}\right]\right|}{\overrightarrow{\mathrm{u}\text{'}}}$

C. C. $\mathrm{d}\left(\mathrm{A};\mathrm{d}\text{'}\right)=\frac{\left[\overrightarrow{\mathrm{AM}\text{'}},\overrightarrow{\mathrm{u}\text{'}}\right]}{\overrightarrow{\mathrm{u}\text{'}}}$

D. D. $\mathrm{d}\left(\mathrm{A};\mathrm{d}\text{'}\right)=\frac{\left|\overrightarrow{\mathrm{AM}\text{'}},\overrightarrow{\mathrm{u}\text{'}}\right|}{\left|\overrightarrow{\mathrm{u}\text{'}}\right|}$

Câu 1:

Phương trình tham số của đường thẳng đi qua điểm $\mathrm{M}\left({\mathrm{x}}_0;{\mathrm{y}}_0;{\mathrm{z}}_0\right)$ và có VTCP $\overrightarrow{\mathrm{u}}=\left(\mathrm{a};\mathrm{b};\mathrm{c}\right)$ là:

A. $\mathrm{d}:\left\{\begin{array}{c}\mathrm{x}={\mathrm{x}}_0+\mathrm{at}\\ \mathrm{y}={\mathrm{y}}_0+\mathrm{bt}\\ \mathrm{z}={\mathrm{z}}_0+\mathrm{ct}\end{array}\right.\left(\mathrm{t}\in \mathrm{Z}\right)$

B. B. $\mathrm{d}:\left\{\begin{array}{c}\mathrm{x}={\mathrm{x}}_0+\mathrm{at}\\ \mathrm{y}={\mathrm{y}}_0+\mathrm{bt}\\ \mathrm{z}={\mathrm{z}}_0+\mathrm{ct}\end{array}\right.\left(\mathrm{t}\in \mathrm{R}\right)$

C. C. $\mathrm{d}:\left\{\begin{array}{c}\mathrm{x}=\mathrm{a}+{\mathrm{x}}_0\mathrm{t}\\ \mathrm{y}=\mathrm{b}+{\mathrm{y}}_0\mathrm{t}\\ \mathrm{z}=\mathrm{c}+{\mathrm{z}}_0\mathrm{t}\end{array}\right.\left(\mathrm{t}\in \mathrm{R}\right)$

D. D. $\mathrm{d}:\left\{\begin{array}{c}\mathrm{x}=\mathrm{a}+{\mathrm{x}}_0\mathrm{t}\\ \mathrm{y}=\mathrm{b}+{\mathrm{y}}_0\mathrm{t}\\ \mathrm{z}=\mathrm{c}+{\mathrm{z}}_0\mathrm{t}\end{array}\right.\left(\mathrm{t}\in \mathrm{Z}\right)$

Câu 2:

Phương trình chính tắc của đường thẳng đi qua $\mathrm{M}\left({\mathrm{x}}_0;{\mathrm{y}}_0;{\mathrm{z}}_0\right)$ và có VTCP $\overrightarrow{\mathrm{u}}=\left(\mathrm{a};\mathrm{b};\mathrm{c}\right)$ là:

A. $\frac{\mathrm{x}-\mathrm{a}}{{\mathrm{x}}_0}=\frac{\mathrm{y}-\mathrm{b}}{{\mathrm{y}}_0}=\frac{\mathrm{z}-\mathrm{c}}{{\mathrm{z}}_0}$

B. B. $\frac{\mathrm{x}-{\mathrm{x}}_0}{{\mathrm{x}}_0}=\frac{\mathrm{y}-{\mathrm{y}}_0}{{\mathrm{y}}_0}=\frac{\mathrm{z}-{\mathrm{z}}_0}{{\mathrm{z}}_0}$

C. C. $\frac{\mathrm{x}-{\mathrm{x}}_0}{\mathrm{a}}=\frac{\mathrm{y}-{\mathrm{y}}_0}{\mathrm{b}}=\frac{\mathrm{z}-{\mathrm{z}}_0}{\mathrm{c}}$

D. D. $\mathrm{d}:\left\{\begin{array}{c}\mathrm{x}={\mathrm{x}}_0+\mathrm{at}\\ \mathrm{y}={\mathrm{y}}_0+\mathrm{bt}\\ \mathrm{z}={\mathrm{z}}_0+\mathrm{ct}\end{array}\right.\left(\mathrm{t}\in \mathrm{R}\right)$

Câu 3:

Trong không gian Oxyz, tìm phương trình tham số trục Oz?

A. $\left\{\begin{array}{c}\mathrm{x}=\mathrm{t}\\ \mathrm{y}=\mathrm{t}\\ \mathrm{z}=\mathrm{t}\end{array}\right.$

B. B. $\left\{\begin{array}{c}\mathrm{x}=\mathrm{t}\\ \mathrm{y}=0\\ \mathrm{z}=0\end{array}\right.$

C. C. $\left\{\begin{array}{c}\mathrm{x}=\mathrm{t}\\ \mathrm{y}=\mathrm{t}\\ \mathrm{z}=0\end{array}\right.$

D. D. $\left\{\begin{array}{c}\mathrm{x}=0\\ \mathrm{y}=0\\ \mathrm{z}=\mathrm{t}\end{array}\right.$

Câu 4:

Đường thẳng $\frac{\mathrm{x}-{\mathrm{x}}_0}{\mathrm{a}}=\frac{\mathrm{y}-{\mathrm{y}}_0}{\mathrm{b}}=\frac{\mathrm{z}-{\mathrm{z}}_0}{\mathrm{c}}$ đi qua điểm

A. $\left(\mathrm{a};\mathrm{b};\mathrm{c}\right)$

B. B. $\left(\mathrm{a};-\mathrm{b};\mathrm{c}\right)$

C. C. $\left({\mathrm{x}}_0;{\mathrm{y}}_0;{\mathrm{z}}_0\right)$

D. D. $\left(-{\mathrm{x}}_0;-{\mathrm{y}}_0;-{\mathrm{z}}_0\right)$

Câu 5:

Trong không gian Oxyz, tìm phương trình tham số trục Ox?

A. $\left\{\begin{array}{c}\mathrm{x}=\mathrm{t}\\ \mathrm{y}=\mathrm{t}\\ \mathrm{z}=\mathrm{t}\end{array}\right.\left(\mathrm{t}\in \mathrm{R}\right)$

B. B. $\left\{\begin{array}{c}\mathrm{x}=\mathrm{t}\\ \mathrm{y}=0\\ \mathrm{z}=0\end{array}\right.\left(\mathrm{t}\in \mathrm{R}\right)$

C. C. $\left\{\begin{array}{c}\mathrm{x}=\mathrm{t}\\ \mathrm{y}=\mathrm{t}\\ \mathrm{z}=0\end{array}\right.\left(\mathrm{t}\in \mathrm{R}\right)$

D. D. $\left\{\begin{array}{c}\mathrm{x}=0\\ \mathrm{y}=0\\ \mathrm{z}=\mathrm{t}\end{array}\right.\left(\mathrm{t}\in \mathrm{R}\right)$

Câu 6:

Đường thẳng $\frac{\mathrm{x}-{\mathrm{x}}_0}{\mathrm{a}}=\frac{\mathrm{y}-{\mathrm{y}}_0}{\mathrm{b}}=\frac{\mathrm{z}-{\mathrm{z}}_0}{\mathrm{c}}$ có một VTCP là:

A. $\left(\mathrm{a};\mathrm{b};\mathrm{c}\right)$

B. B. $\left(\mathrm{a};-\mathrm{b};\mathrm{c}\right)$

C. C. $\left({\mathrm{x}}_0;{\mathrm{y}}_0;{\mathrm{z}}_0\right)$

D. D. $\left(-{\mathrm{x}}_0;-{\mathrm{y}}_0;-{\mathrm{z}}_0\right)$