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 = L u_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. USING MAT LAB CODE: 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 = 0.7 r_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 r_2, the second r_1, the third V, and the fourth S.

Solution

Enter the MATLAB code to determine a vector of length 18 in the direction os the vector u:

%u vector

u = [7 -4 -11];

%length

L =18;

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

Output:

wL =

9.2388 -5.2793 -14.5181

The required vector is wL = 9.2388i-5.2793j-14.5181k