Scalar product - practice problems - last page
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 26
- Angle between line and plane
Find the angle between the line given parametrically by x = 5 + t y = 1 + 3t z = -2t t ∈ R and the plane given by the 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. - Cuboids
Two separate cuboids with different orientations are 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 the 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 = (-1, 24) and v = (-8, -21) - Triangle
Plane coordinates of vertices: K[9, 5] L[-4, 8] M[3, 20] give Triangle KLM. Calculate its area and its interior angles.
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