Equation + vector - practice problems
Number of problems found: 20
- EE school boarding
Three vectors, A, B, and C, are related as follows: A/C = 2 at 120 deg, A + B = -5 + j15, C = conjugate of B. Find C. - Determine 82034
The vectors a = (3, -2), b = (-1, 5) are given. Determine the vector c for which a. c = 17; c = 3 - 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. - Introduced 81104
The * (asterisk) operation assigning one number to two pairs of numbers is introduced as follows: (a, b)*(c, d) = ac+bd We know that: (x,2)*(-1, v) = -1 and (2,-1)*(u, v)=5 and (u, v)*(1,1)=-2 What is (1,2)*(x, y) equal to if y=3?
- 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 - Direction vector
The line p is given by the point P [- 0,5; 1] and the direction vector s = (1,5; - 3) determines: A) value of parameter t for points X [- 1,5; 3], Y [1; - 2] lines p B) whether the points R [0,5; - 1], S [1,5; 3] lies on the line p C) parametric equations - 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) - Vector equation
Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent - Angled cyclist turn
The cyclist passes through a curve with a radius of 20 m at 25 km/h. How much angle does it have to bend from the vertical inward to the turn?
- Parametric form
Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. - Perpendicular and parallel
Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular and parallel lines. What angle does each line make with the x-axis, and find the angle between the lines? - Axial symmetry
Find the image A' of point A [1,2] in axial symmetry with the axis p: x = -1 + 3t, y = -2 + t (t = are real number) - Downstream 7002
A rowboat sailing down a river covers a distance of 120 m downstream in 12 s and upstream in 24 s. Find the magnitude of the ship's velocity relative to the water and the current in the river. Both speeds are constant. - Equation of the circle
Find the equation of the circle with the center at (1,20), which touches the line 8x+5y-19=0
- Parametrically 6400
Find the angle of the line, which is determined parametrically x = 5 + t y = 1 + 3t z = -2t t belongs to R and the plane, which is determined by the general equation 2x-y + 3z-4 = 0. - Three points 2
The three points are A(3, 8), B(6, 2), and C(10, 2). Point D is such that the line DA is perpendicular to AB, and DC is parallel to AB. Calculate the coordinates of D. - Parametric equations
Write the parametric equations of height hc in triangle ABC: A = [5; 6], B = [- 2; 4], C = [6; -1] - Equation 2604
The given triangle is ABC: A [-3; -1] B [5; 3] C [1; 5] Write the line equation that passes through the vertex C parallel to the side AB. - 3d vector component
The vector u = (3.9, u3), and the length of the vector u is 12. What is, is u3?
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