Find the unit vector that is perpendicular to both i + 2j+ k and 3i-4j+2k.

A5 foot by 5 foot box culvert is buried 6 feet beneath the surface of the ground. a crosssection of this very long culvert (into and out of the page) is illustrated below. assume that the soil in which the culvert is buried has the following properties: jt = 120 pcf, w = 12%, ko = 0.50, ka = 0.33, and kp = 3.00. calculate the total horizontal force per unit length of culvert (fh) felt on one of the vertical faces of the culvert.

Aturntable that spins at a constant 74.0 rpm takes 3.10 s to reach this angular speed after it is turned on. find its angular acceleration (in rad/s2), assuming it to be constant, and the number of degrees it turns through while speeding up.

Abig box of sausages (30 kg) are lifted from the ground to the top shelf of the freezer. if the box is lifted at a constant speed, a distance of 1.75 m, what work is done by gravity?