Analytic geometry + vector - practice problems
Number of problems found: 56
- Vector
Determine coordinates of the vector u=CD if C[12;-8], D[6,20]. - Place vector
Place the vector AB if A (3, -1), B (5,3) in point C (1,3) so that AB = CO. - Points collinear
Show that the point A(-1,3), B(3,2), C(11,0) are col-linear. - Vector perpendicular
Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1) - Coordinates of vector
Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5) - Vector v4
Find the vector v4 perpendicular to the vectors v1 = (1, 1, 1, -1), v2 = (1, 1, -1, 1) and v3 = (0, 0, 1, 1) - Coordinates of square vertices
The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square. - Linear independence
Determine if vectors u=(-4; -10) and v=(-2; -7) are linear dependents. - Direction 7999
A (5; -4) B (1; 3) C (-2; 0) D (6; 2) Calculate the direction vector a) a = AB b) b = BC c) c = CD - Parametric equations
Write the parametric equations of height hc in triangle ABC: A = [5; 6], B = [- 2; 4], C = [6; -1] - Vector sum
The magnitude of the vector u is 12 and the magnitude of the vector v is 8. The angle between vectors is 61°. What is the magnitude of the vector u + v? - Line
Line p passes through A[5, -3] and has a direction vector v=(2, 3). Is point B[3, -6] on the line p? - Ascend vs. descent
Which function is growing? a) y = 2-x b) y = 20 c) y = (x + 2). (-5) d) y = x-2 - Angle of the body diagonals
Using the vector dot product calculate the angle of the body diagonals of the cube. - Rectangle 39
Find the perimeter and area of the rectangular with vertices (-1, 4), (0,4), (0, -1), and (-4, 4) - Angle between vectors
Find the angle between the given vectors to the nearest tenth degree. u = (6, 22) and v = (10, -11) - Intersection 81611
Given a triangle ABC: A (-1,3), B(2,-2), C(-4,-3). Determine the coordinates of the intersection of the heights and the coordinates of the intersection of the axes of the sides. - Perpendicular 28823
Points A(1,2), B(4,-2) and C(3,-2) are given. Find the parametric equations of the line that: a) It passes through point C and is parallel to the line AB, b) It passes through point C and is perpendicular to line AB. - Triangle 82
Triangle PQR has vertices located at (2, 2), (5, -4), and (-4, -1). What type of triangle is triangle PQR? - Quadrilateral PQRS
PQRS is a quadrilateral with P(4,4), S(8,8), and R(12,8). If vector PQ=4*vector SR, find the coordinates of Q. Solve it
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