Find the angle between v and w Round to one decimal place if

Find the angle between v and w. Round to one decimal place, if necessary. v = 2i + j - 2k and w = i + 3j + 3k 92.9 degree 94.4 degree 89.6 degree 78.3 degree 92 degree Find the direction angles of the vector. Round to the nearest degree, if necessary. v = 12i + 6j + 4k alpha = 23 degree, beta = 63 degree, gamma = 72 degree alpha = 86 degree, beta = 88 degree, gamma = 89 degree alpha = 19 degree, beta = 62 degree, gamma = 72 degree alpha = 31 degree, beta = 65 degree, gamma = 73 degree alpha = 51 degree, beta = 67 degree, gamma = 83 degree

Solution

8) v = 2i + j - 2k

w = i + 3j + 3k

IvI = 3

IwI = sqrt(19)

v.w = 2 + 3 - 6 = -1

Now Angle = arccos[v.w/IvI*IwI] = 94.4 degree

9) |a| = a_x² + a_y² + a_z² = 12² + 6² + 4² = 144 + 36 + 16 = 196 = 14

cos = 12/14 =======> = 31

cos = 6/14 ======> = 64.6

cos = 4/14 ======> = 73.4

Option D)