Two forces act at a point in the xy-plane: F₁ = 50 N at 25° and F₂ = 270 N at 240°, both measured anticlockwise from the positive x-axis. Find the direction φ of their resultant, measured anticlockwise from the positive x-axis (between 0° and 360°).
Find the x-component ûx of the unit vector û that points in the direction of a = (3, −7, 6).
Find the angle θ between the vectors a = (−1, 1, 6) and b = (−3, 1, −6), in degrees.
Find the dot product a·b of a = (7, 4, 1) and b = (−1, 4, −3).
The unit vector n̂ is perpendicular to both a = (3, 2, 4) and b = (−4, −4, 2) and has a positive z-component. Find its y-component n̂y.
Find the volume V of the parallelepiped whose edges from one corner are a = (5, −1, 4), b = (−5, 4, −2) and c = (1, −2, −4).
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