Jika A = <-6, 2, 5>, B = <-8, 3, 4> dan C = A-B, apakah sudut antara A dan C?

Jika A = <-6, 2, 5>, B = <-8, 3, 4> dan C = A-B, apakah sudut antara A dan C?
Anonim

Jawapan:

# alpha ~ = 63 ^ o #

Penjelasan:

#C = (- 6 - (- 8)), (2-3), (5-4) #

# C = <2, -1,1> #

# A * C = A_x * B_x + A_y * B_y + A_z * B_z #

# A * C = -12-2 + 5 = -9 #

# || A || = sqrt (36 + 4 + 25) "" || A || = sqrt65 #

# || C || = sqrt (4 + 1 + 1) "" || C || = sqrt6 #

# A.C = || A || * || C || * cos alpha #

# -9 = sqrt65 * sqrt6 * cos alpha = #

# -9 = sqrt (65 * 6) * cos alpha #

# -9 = sqrt390 * cos alpha #

# -9 = 19,74 * cos alpha #

#cos alpha = -9 / (19,74) #

#cos alpha = 0.445927051672 #

# alpha ~ = 63 ^ o #