Scalar product - practice problemsDirection: Solve each problem carefully and show your solution in each item.
Number of problems found: 23
- Scalar product
Calculate the scalar product of two vectors: (2.5) (-1, -4)
- Matrices 2
Suppose A=(1 6 3 −2) B=(4 −3 −4 3) find 2A+3B
- 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 v4
Find the vector v4 perpendicular to 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.
- Angle of the body diagonals
Using the vector dot product calculate the angle of the body diagonals of the cube.
- Decide 2
Decide whether points A[-2, -5], B[4, 3], and C[16, -1] lie on the same line
- 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°
- Angle between vectors
Find the angle between the given vectors to the nearest tenth degree. u = (6, 22) and v = (10, -11)
- 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.
- 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 magnitude of the angle between two vectors u = (3; -5) and v = (10; 6)
- 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.
- 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
- 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, and the distance between the vectors.
- Find the 5
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.
- Find the 10
Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular and parallel. What angle does each line make with the x-axis, and find the angle between the lines?
- 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