Bài tập Xác định phương trình đường thẳng khi biết yếu tố song song lớp 12 (có lời giải)

A. \(\frac{{x - 1}}{4} = \frac{y}{5} = \frac{{z - 1}}{{ - 1}}\);

B. \(\frac{{x + 1}}{2} = \frac{y}{3} = \frac{{z + 1}}{{ - 1}}\);

C. \(\frac{{x - 1}}{2} = \frac{y}{3} = \frac{{z - 1}}{{ - 1}}\);

D. \(\frac{{x + 1}}{4} = \frac{y}{5} = \frac{{z + 1}}{{ - 1}}\).

A. \(\left\{ \begin{array}{l}x = 1\\y = 3 + t\\z = 4\end{array} \right.\);

B. \(\left\{ \begin{array}{l}x = 1 - t\\y = 3\\z = 4\end{array} \right.\);

C. \(\left\{ \begin{array}{l}x = 1\\y = 3\\z = 4 + t\end{array} \right.\);

D. \(\left\{ \begin{array}{l}x = 1\\y = 3 + t\\z = 4 + t\end{array} \right.\).

A. \(\left\{ \begin{array}{l}x = - 1\\y = 2\\z = 2 + t\end{array} \right.\);

B. \(\left\{ \begin{array}{l}x = - 1\\y = t\\z = 2\end{array} \right.\);

C. \(\left\{ \begin{array}{l}x = - 1 + t\\y = 2\\z = 2\end{array} \right.\);

D. \(\left\{ \begin{array}{l}x = - 1 + t\\y = 2\\z = 2 + t\end{array} \right.\).

A. \(\frac{{x + 1}}{2} = \frac{{y + 1}}{1} = \frac{z}{1}\);

B. \(\frac{{z + 1}}{4} = \frac{{y + 1}}{1} = \frac{z}{1}\);

C. \(\frac{{x - 1}}{2} = \frac{{y - 1}}{1} = \frac{z}{{ - 1}}\);

D. \(\frac{{x - 1}}{4} = \frac{{y - 1}}{1} = \frac{z}{1}\).

A. \(x - 2y + z = 0\);

B. \(\left\{ \begin{array}{l}x = - 2t\\y = - 1 + t\\z = 3 + t\end{array} \right.\);

C. \(\frac{x}{{ - 2}} = \frac{{y + 1}}{1} = \frac{{z - 3}}{1}\);

D. \(\frac{{x - 1}}{{ - 2}} = \frac{y}{1} = \frac{{z - 1}}{1}\).

A. \(\frac{x}{1} = \frac{{y - 1}}{1} = \frac{{z + 1}}{2}\);

B. \(\frac{x}{1} = \frac{{y - 1}}{{ - 1}} = \frac{{z + 1}}{2}\);

C. \(\frac{{x - 1}}{1} = \frac{{y - 1}}{{ - 1}} = \frac{{z + 1}}{2}\);

D. \(\frac{x}{1} = \frac{{y - 2}}{{ - 1}} = \frac{{z + 2}}{2}\).

A. \(\left\{ \begin{array}{l}x = 3 + t\\y = 2t\\z = 1 - t\end{array} \right.\);

B. \(\left\{ \begin{array}{l}x = 2 + t\\y = - t\\z = - 1\end{array} \right.\);

C. \(\left\{ \begin{array}{l}x = 1 + 2t\\y = - 1\\z = - t\end{array} \right.\);

D. \(\left\{ \begin{array}{l}x = 3 + t\\y = 1 + 2t\\z = - t\end{array} \right.\).

A. \(\frac{{x - 1}}{{ - 2}} = \frac{{y - 2}}{4} = \frac{{z + 1}}{{ - 2}}\);

B. \(\frac{{x - 1}}{1} = \frac{{y - 2}}{3} = \frac{{z + 1}}{5}\);

C. \(\frac{{x - 1}}{1} = \frac{{y - 2}}{{ - 2}} = \frac{{z + 1}}{{ - 1}}\);

D. \(\frac{x}{1} = \frac{{y + 2}}{2} = \frac{{z - 3}}{1}\).

A. \(\overrightarrow u = \left( { - 1; - 1;1} \right)\);

B. \(\overrightarrow u = \left( {2; - 1;1} \right)\);

C. \(\overrightarrow u = \left( {1; - 2;1} \right)\);

D. \(\overrightarrow u = \left( { - 1; - 1; - 2} \right)\).

A. 6;

B. −6;

C. 9;

D. −9.