Consider the vector functions c(t) = t³+ costj – t² e−2/ a(t) = and calculate 1 е −2t+7+4te² / t d dt (exd) (č x d)
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- A stone is thrown from a rooftop at time t=0 seconds. Its position at time t is given by r(t)=6ti−4tj+(9.8−4.9t^2)k. The origin is at the base of the building, which is standing on flat ground. Distance is measured in meters. The vector i points east, j points north, and k points up.(a) How high is the rooftop? meters.(b) When does the stone hit the ground? seconds.(c) Where does the stone hit the ground? (in meters)(d) How fast is the stone moving when it hits the ground? (in meters per second)Find the coordinates of a point P on the line and a vector v parallel to the line (x + 3)/5 = y/8 = (z − 3)/6solve for th e vector x in terms of the vectors a and b. x - a= 2(x - 2a)
- Express the vector = H as a linear combination of x = = [1] and [1] eFind the vector equation of the line that passes through the point (1, 5) and is parallel to the line r = (3 + 7t)i + (1 − 3t)j.find the vector equation for the line through the point A = (5, -2, 1) at t = 0. and B = (-3, 1, -2) at t = 1.