comp =?
projab =?,?,?
Answer 1
The scalar projection = (scalar product of a,b ) / magnitude of
a=
a . b/mag.a
Therefore, the scalar projection of b onto a is the component of b onto
meaning of a = comp(a)b = ab/mag. a = ii + j.-j + kk = 1/v
3.
The vector projection is = scalar projection unit vector* in
direction of a = (a point.b)/mag.a * a / mag.a = a.point.b / (mag.a)^2
* a =
{1/ (v3 .*v3 )}*(vector a) = (1/ v 3)^2 *( i + j + k ) = 1/3 ( i +
j + k)
So proj(a)b = 1/3 (i + j + k)
If a = (x0, y0, z0) and b = (x1, y1, z1) then the vector projection
from b to a is given by ka
where k = (x0x1 + y0y1 + z0z1)/(x0^2 + y0^2 + z0^2)
The scalar projection is only the magnitude of ka.
In this case,
A=(1,1,1),
B=(1,-1,1)
K=(1-1+1)/(1+1+1)
K=1/3
VECTOR PROJECTION
It’s b=ka
i-j+k=1/3(i+j+k)
the scalar projection is only the magnitude of ka