Homework

Theoretical material: Function. The limit function. Fundamental theorems on limits. Infinitely small and infinitely large quantities.

Solve problems:

1. Vertex of triangle ABC are given: . Define coordinates of a point of intersection of medians of a triangle.

2. Two vertices of a triangle А(3;8) and В(10;2) and point of intersection of medians of M (1; 1) are given. Find coordinates of thirds of vertex of a triangle.

3. Make the equation of the line passing through the point of А(-2;1):

а) parallel to the axis Оу;

b) forms an angle with the Ох -axis;

c) parallel to the bisector of the first quadrantal angle;

d) perpendicular to the straight line 6x-y +2 = 0;

d) cut off on the y-axis segment length of 5.

4. Find the areas of the triangle with vertices P = (2, 1, 0), Q = (3, 4, 5), R = (6, 1, 2).

5. Find the distance from (2, 4 –1) to the plane z = 2 x + y + 3. Give parametric equations of the line that passes through the origin and through the intersection of the lines L₁: x = 3 + 2 t, y = –4 t, z = –3 + t and L₂: x = 3 + 10 t, y = –25 + 5 t, z = 4 – 2 t.

6. Find the measures of the angles between the diagonals of the rectangle whose vertices are

7. Let . Find the a) component form and b) magnitude (length) of the vector.

a). ; b). .

Поиск по сайту: