Soru # 94346

Cevap:

#hat (PQR) = cos ^ (- 1) (27 / sqrt1235) #

Açıklama:

İki vektör olmak #vec (AB) # ve #vec (AC) #:

#vec (AB) * vec (AC) = (AB) (AC) cos (şapka (BAC)) #

# = (X_ (AB) x_ (AC)) + (Y_ (AB) Y_ (AC)) + (Z_ (AB) Z_ (AC)) #

Sahibiz:

# P = (1; 1: 1) #

#Q = (- 2, 2, 4) #

# R = (3, -4, 2) #

bu nedenle

#vec (QP) = (x_P-x_Q; y_P-y_Q; z_P-z_Q) = (3, 1; -3) #

#vec (QR) = (x_R-x_Q; y_R-y_Q; z_R-z_Q) = (5; -6, -2) #

ve

# (QP) sqrt ((x_ (QP)) ^ 2 + (Y_ (QP)) ^ 2 + (Z_ (QP)) ^ 2) = sqrt (9 + 1 + 9) = sqrt (19) # =

# (QR) sqrt ((x_ (QR)) ^ 2 + (Y_ (QR)) ^ 2 + (Z_ (QR)) ^ 2) = sqrt (25 + 36 + 4) = sqrt (65) # =

Bu nedenle:

#vec (QP) * vec (QR) = sqrt19sqrt65cos (şapka (PQR)) #

#=(3*5+(-1)(-6)+(-3)(-2))#

#rarr cos (şapka (PQR)) = (15 + 6 + 6) / (sqrt19sqrt65) = 27 / sqrt1235 #

#rarr şapka (PQR) = cos ^ (- 1) (27 / sqrt1235) #