3. . .
1. 2
2. 1) 
. 
.
2) 
( 
)? 
.
3) 
, 
, 
.
3.1.
1. ( ).
( ) || ,
, .
, .
, .
2. λ = λ, |b| = |λ| | |, , λ> 0, , λ< 0.
b = + b, .
b = + (-).
3. (, ) (, , z) , .
= (, , z)
= xi + yj + zk
i, j, k (), Ox, Oy, Oz; |i | = |j| =|k| = 1.
4. | | :
| | = 2+2
| |= 2+2+z2
5. cos α, cos β, cos γ, α, β, γ , Oy, Oz :
cos α=x/ x2+y2+z2, cos β=y/ x2+y2+z2, cos γ=z/ x2+y2+z2
cos2 α + cos2 β + cos2 γ= 1.
6. = (1, 1, z1)
b = (2, 2,z2) λ :
a + b =(1, 1, z1)+(2, 2,z2)= (xl+x2, y1+ y2, zl+z2), λ = λ(1, 1, z1) = (λ1, λ1, λz1).
7. I
/ = |a| cosφ, φ /.
8. (, )
(, b)=ab=|| |b| cosφ
= (1, 1, z1) b= (2, 2,z2) :
(,b)=ab=xlx2+y1y2+z1z2.
= (,,z) :
(,)=2 =||2 =x2+y2+z2.
9. φ = (1, 1, z1) b(2, 2,z2) = :
cos φ=(, b)/ || |b|= xlx2+y1y2+z1z2/ x12+y12+z12* x22+y22+z22.
10. , b , , . . b = 0.
|
|
|
11. = (1, 1, z1) b= (2, 2,z2): ()
b=ka, x2/x1=y2/y1=z2/z1=k
()
b = 0 xlx2+y1y2+z1z2=0
