Задача 32309 ...

miltary73

2018-12-22 18:31:28

1. Дано:

|a| = 1
|b| = 2
a ⊥ b

Найти: (a - 2b) / (3a + b)

2. Найти проекцию вектора

c = i + 2j - k на вектор
c = (a x b), если

a = i + 2k и b = -i + 5k

sova

2018-12-22 22:48:04

★

1.
(vector{a}-2vector{b})*(3vector{a}+vector{b})=

=3vector{a}*vector{a} -6vector{b}*vector{a}+
+vector{a}*vector{b}-2vector{b}*vector{b}=

=3*|vector{a}|*|vector{a}|cos)^(o) -6* |vector{b}|*|vector{a}|cos90^(o)+
+|vector{a}|*|vector{b}|*cos90^(o)-2*|vector{b}|*|vector{b}|*cos0^(o)=

=3*1*1*1-6*2*1*0+1*2*0-2*2*2*1=3-8=-5

2.
vector{c}=[vector{a}×vector{b}] = - 7j ( cм. приложение)

пр_(vector{c})vector{p}=vector{p}*vector{c}/|vector{c}|=

=(1*0+2*(-7)+(-1)*0)/7=-2