Find the direction vector and the normal vector of a straight line *p*, if :

Find the parametric, the general and the slope-intercept equation of a straight line *p* passing through the points :

A straight line *p* with a direction vector ** d** and a normal vector

*passes through the point*

**n***K*. Find the parametric, the general and the slope-intercept equation of a straight line

*p*, if :

Find the parametric, the general and the slope-intercept equation of a straight line *p*, which passes through the point *M*, if the slope angle between a straight line *p* and the *x-*axis is *φ* :

Transform the parametric equations of the straight line into the general equation and into the slope-intercept equation :

Transform the general equation of the straight line into the parametric equations and into the slope-intercept equation :

Transform the slope-intercept equation of the straight line into the parametric equations and into the general equation :

Find the general equation and the slope-intercept equation of a straight line, which passes through the point *L* and which is parallel to the given straight line *p* :

Find the general equation and the slope-intercept equation of a straight line, which passes through the point *N* and which is perpendicular to the given straight line *p* :

Find the slope angle of a straight line given by the equation :

Decide whether the given straight lines *p* and *q* are parallel or perpendicular to each other :

(work with normal vectors of the straight lines)

Consider the two points *A* [3;2], *B* [–1;–1] and the vector *a** = *(12;–5), where * a = C* –

*B*.

**a)** Find the coordinates of the point *C*.**b)** Prove that the points *A*, *B*, *C* are vertices of a triangle.**c)** Find the general equations of straight lines on which lie the sides of the triangle *ABC*.**d)** Find the general equations of straight lines on which lie the medians of the triangle *ABC*.**e)** Find the general equations of straight lines on which lie the altitudes of the triangle *ABC*.**f)** Find the parametric equations of the straight line passing through the midpoints of the line segments *AC* and *BC*.**g)** Find the slope-intercept equation of the straight line passing through the point *A* and parallel to the straight line *BC*.**h)** Find the coordinates of the centroid *T*.**i)** Find the perimeter of the triangle *ABC*.**j)** Find the area of the triangle *ABC*.

Find the general equation of the perpendicular bisectors of line segments *AB*, *AC* and *BC*, if *A* [2;5], *B* [–3;9], *C* [6;12].

Prove that the points *A* [3;4], *B* [–1;2], *C* [1;3], *D* [–5;0] lie on one straight line. Find the parametric, the general and the slope-intercept equation of the straight line.

Find the parametric equations of a straight line passing through the point *A* [4;–1;9] which is parallel to

Find the parametric equations of a straight line *p* passing through the point *A* [2;–1;2] perpendicularly to the plane *π*: *x* – *y* + *z* + 13* = *0.

Find the parametric equations and the general equation of a plane *ρ* = *ABC*, *A* [–4;0;2], *B* [–2;1;1], *C* [1;–3;–2].

Find the general equation of a plane α which passes through the point *A* [2;1;4] and which is parallel to the plane *β*: *x* – 2*y* + 5*z* + *d = *0.

Find the general equation of a plane σ which passes through the point *A* [1;2;0] and which is perpendicular to the straight line *p*: *x = *3 – *t*; *y = *4 + 2*t*; *z = *1 – 2*t*; *t*∈**R**.

Consider a regular square pyramid *ABCDV* with vertices *D* [0;0;0], *A* [4;0;0], *B* [4;4;0], *V* [2;2;6]. Find the general equation of a plane *BCV*.

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