Chapter 11.2, Problem 29E

Parametrize the line that passes through the point (1, 2, 3) parallel to the vector v =-3i + 7k.

Let f(x, y) = x64. Round the components of your answers to three decimal places. (a) At the point ( – 2, 1), find a unit vector in the direction of maximum rate of change. 7 i + i i (b) At the point ( – 2, 1), find a unit vector in the direction of minimum rate of change. 7 + i

Let A = (0, 0, 0) and vector v = (-3, 0, 1). Find vector equation of the line containing the point A and parallel to the vector v.

Subtracting the two equations, find a vector equation for the curve of intersection between y= 4x2+(3/4)z2 and y-1= 3x2+(1/2)z2 for x>0. Find and simplify the tangential component of acceleration for your curve.

the position vector r describes the path of an object moving in space. (a) Find the velocity vector, speed, and acceleration vector of the object. (b) Evaluate the velocity vector and acceleration vector of the object at the given value of t. r(t) = ⟨t, −tan t, e^t⟩ t = 0

V(t)=?r(t)=?

(14) The straight line L passes through the origin O and is in the direction i+mj. The straight line L' passes through the point A whose position vector is ai and is in the direction i+m'j. Write down the vector equations of L and L' and find the position vector of their point of intersection.

An object is moving in space with an acceleration 参数划分是指对负极 a(t) = -t i+3j+ (t – 3) k. Find the velocity vector v(t) and position vector r(t) of the object at any time t if at time t = 0, the object is at the point (0, 2. 1) and it has the velocity v(0) = i- j+ 2k. 问题的 极性问题是预期答享 于是和否的问题(因此 它们也称为是-否问 please ignore the background text Bartleby and solve black part only 极性问题可以是肯定的或否定的。 否定问题是非中性或有偏见的问题 “提问者偏向于基于原始信念的肯 定句答案或基

Brazilian soccer star Marta has a penalty kick in the quarter-final match. She kicks the soccer ball from ground level with the (x, y)-coordinates (76, 21) on the soccer field shown in the figure and with initial velocity vo = 8i - 4j+23k ft/s. Assume an acceleration of 32 ft/s² due to gravity and that the goal net has a height of 8 ft and a total width of 24 ft. 105 ft 1 105 ft r₁ = rj = rk = 165 ft Determine the position function that gives the position of the ball t seconds after it is hit. (Use symbolic notation and fractions where needed.) r(t) = ri(t)i + rj(t)j + rk(t)k Incorrect 81+76 -41+21 ↓ 23r+1672² 165 ft 12 12