A vector wL of length L in the direction of a vector u xi

A vector w_L of length L in the direction of a vector u = xi + yj + zk can determined by w_L = Lu_n (multiplying a unit vector in the direction of u by L). The unit vector u_n in the direction of the vector u is given by u_n = xi + yj + zk/squareroot x^2 + y^2 + z^2. By writing one MATLAB command, determine a vector of length 18 in the direction of the vector u = 7i - 4j - 11k. The volume V and the surface area S of a torus-shaped water tube are given by: V = 1/4 pi^2(r_1+r_2)(r_2-r_1)^2 and S = pi^2(r^2_2 - r^2_1) If r_1 = 0.7r_2, determine V and S for r_2 =12, 16, 20, 24, and 28 in. Display the results in a four-column table where the first column is r_2, the second r_1 the third V, and the fourth S.

Solution

3.77)

u=[7 -4 -11]

L= 18;

wL=L.*u./sqrt(sum(u.^2))

mat lab output:

wL=

9.2388 -5.2793 -14.5181