Plane geometry

1003061206

Level:

Find the value of a parameter

a

, such that the line

a x - 6 y - 15 = 0

is parallel to the line

y = - \frac{2}{3} x + 4

a = - 4

a = 4

a = - \frac{2}{3}

a = - 2

1003061208

Level:

We are given a straight line

q = {[1 + 3 t; 2 - 2 t], t \in R}

. Specify the value of a parameter

a

such that the line

5 x + a y + 1 = 0

is parallel to

q

a = 7.5

a = 2.5

a = - 7.5

a = - 2.5

1003061304

Level:

Determine the relative position of the lines

p : 4 x - 3 y + 9 = 0

and

\begin{aligned} q : x & = 6 + 3 t, \\ y & = 11 + 4 t, \end{aligned}

where

t \in R

identical lines,

p = q

parallel different lines,

p ∥ q; p \neq q

intersecting lines,

p \cap q = {[0; 3]}

intersecting lines,

p \cap q = {[6; 11]}

1003061305

Level:

Determine the relative position of the lines

p : 4 x + 6 y - 5 = 0

and

q : y = - \frac{2}{3} x - 6

parallel different lines,

p ∥ q; p \neq q

identical lines,

p = q

intersecting lines,

p \cap q = {[0; \frac{5}{4}]}

intersecting lines,

p \cap q = {[0; \frac{5}{6}]}

1003061306

Level:

Determine the relative position of the lines

p : 2 x - 3 y + 7 = 0

and

\begin{aligned} q : x & = 2 + t, \\ y & = - 3 t, \end{aligned}

where

t \in R

intersecting lines,

p \cap q = {[1; 3]}

identical lines,

p = q

parallel different lines,

p ∥ q; p \neq q

intersecting lines,

p \cap q = {[7; 7]}

1103061201

Level:

From the following list, choose parametric equations, that do not represent the straight line passing through the points

A

and

B

(see the picture).

\begin{aligned} p : x & = 2 + 4 t, \\ y & = 6 + 2 t; t \in R \end{aligned}

\begin{aligned} p : x & = 2 + 2 t, \\ y & = 1 + t; t \in R \end{aligned}

\begin{aligned} p : x & = 6 + 4 t, \\ y & = 3 + 2 t; t \in R \end{aligned}

\begin{aligned} p : x & = 2 - 2 t, \\ y & = 1 - t; t \in R \end{aligned}

\begin{aligned} p : x & = 4 + 4 t, \\ y & = 2 + 2 t; t \in R \end{aligned}

1103061202

Level:

A straight line

p

is given by the point

A

and the normal vector

\vec{n}

(see the picture). Find its equation in general form.

p : 2 x - 5 y - 6 = 0

p : 2 x + 5 y - 6 = 0

p : 5 x - 2 y - 15 = 0

p : 5 x + 2 y - 15 = 0

1103061203

Level:

A straight line

p

is given by the point

A

and the direction angle

φ

(see the picture). Choose the equation of the line

p

in the slope-intercept form.

p : y = - \sqrt{3} x + 3

p : y = \sqrt{3} x + 3

p : y = 1.7 x + 3

p : y = - 1.7 x + 3

1103061204

Level:

From the following list choose the equation of a straight line that passes through the given point

K

and is not parallel to the given line

m

(see the picture).

g : y = - \frac{3}{2} x + \frac{13}{2}

b : 2 x - 3 y - 13 = 0

f : y = \frac{2}{3} x - \frac{13}{3}

\begin{aligned} q : x & = 5 + 3 t, \\ y & = - 1 + 2 t; t \in R \end{aligned}

1103061205

Level:

From the following list choose the equation of a straight line that passes through the given point

K

and is not perpendicular to the given line

m

(see the picture).

r : y = \frac{2}{3} x - \frac{13}{3}

p : 3 x + 2 y - 13 = 0

s : y = - \frac{3}{2} x + \frac{13}{2}

\begin{aligned} q : x & = 5 + 2 t, \\ y & = - 1 - 3 t; t \in R \end{aligned}

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