vectors

the angle between a and b is 90°, find the length of projection of a on the line of b.
(a and b are vectors). a=3i+j, b=i-3j.
It should be 0. Since a and b is 90°
The projection of a on the line of b should be only a point.
Mathematically
the length of projection of a on the line of b
=a.b
=|a||b|cos(the angle between a and b)
=|a||b|cos(90)
=2*2*0
=0

2007-02-04 16:23:35 補充：
寫錯少少添Since the angle between a and b is 90°|a||b|cos(90)=√10*√10*0=0

If the angle between a and b is 90, the length of projection of a on the line of b is equal to 0. You can draw the projection yourself.

Let the angle between a and b be C.

a . b = |a| * |b| cos C [a . b is dot product.]

(3i + j) . (i - 3j) = (|a| * cos C) * |b|

3 - 3 = (projection of a on the line of b) * |b|

0 = (projection of a on the line of b) * |b|

projection of a on the line of b = 0 / |b| = 0

其實唔使計架...
任何vector互相垂直都係0架啦
(cos90°= 0 嘛)