מהי ההקרנה של (32i-38j-12k) אל (18i -30j -12k)?

תשובה:

#vec c = <24,47i, -40,79j, -16,32k> #

הסבר:

#vec a = <32i, -38j, 12k> #

#vec b = <18i, -30j, 12k> #

#vec a * vec b = 18 * 32 + 38 * 30 + 12 * 12 = #

#vec a * vec b = 576 + 1140 + 144 = 1860 #

# | b | = sqrt (18 ^ 2 + 30 ^ 2 + 12 ^ 2) # #

# | b | = sqrt (324 + 900 + 144) #

# | b | = sqrt1368 #

#vec c = (vec a * vec b) / (| b * * | b *) * vec b #

#vec c = 1860 / (1368 * sqrt 1368) <18i, -30j, -12k>

#vec c = 1860/1368 <18i, -30j, 12k> #

#vec c = <(1860 * 18i) / 1368, (-1860 * 30j) / 1368, (- 1860 * 12k) / 1368>

#vec c = <24,47i, -40,79j, -16,32k> #