# Scalar product - practice problems

#### Number of problems found: 22

- Vectors

Find the magnitude of the angle between two vectors u = (3; -5) and v = (10; 6) - Space vectors 3D

The vectors u = (1; 3; -4), v = (0; 1; 1) are given. Find the size of these vectors, calculate the angle of the vectors, the distance between the vectors. - Perpendicular projection

Determine the distance of a point B[1, -3] from the perpendicular projection of a point A[3, -2] on a straight line 2 x + y + 1 = 0. - Determines: 33451

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 - 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. - Vector v4

Find the vector v4 perpendicular to vectors v1 = (1, 1, 1, -1), v2 = (1, 1, -1, 1) and v3 = (0, 0, 1, 1) - Decide 2

Decide whether points A[-2, -5], B[4, 3] and C[16, -1] lie on the same line - 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 - Angle of the body diagonals

Using vector dot product calculate the angle of the body diagonals of the cube. - Parallel and orthogonal

I need math help in this problem: a=(-5, 5 3) b=(-2,-4,-5) (they are vectors) Decompose the vector b into b=v+w where v is parallel to a and w is orthogonal to a, find v and w - 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. .. - Find the 10

Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular, parallel, what angle does each of the lines make with the x-axis, find the angle between the lines? - 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. - Scalar product

Calculate the scalar product of two vectors: (2.5) (-1, -4) - Find the 5

Find the equation of the circle with 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 A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB, and DC is parallel to AB. Calculate the coordinates of D. - Cuboids

Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633) - Scalar dot product

Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120°

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