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Hey, I'm stuck on one problem for my homework (LAST ONE!!) It seems really simple but I can't figure it out. Here it is:
Express the vector A = 2i - 3j + 5k as a sum A = B + C, where B is parallel to the vector V = 3i -2j +5k and C is perpendicular to V.
Here's what I know:
B x V = 0, because B is parallel to V
C (dot) V = 0, because C is perpendicular to V
However I can't find a way to apply the above :confused:
Thanks! :o
B=[(A.V)/(V.V)]V and C=A-B, where (A.V) is the dot product of A and V.
Hello, Raman!
There are formulas for this problem . . .
Quote:
Express the vector: .A .= .2i - 3j + 5k .as a sum .A .= .B + C,
where B is parallel to the vector V .= .3i - 2j + 5k, and C is perpendicular to V.
Code:*
A * :
* : C
* :
*---------------+-------*
: - - - B - - - :
: - - - - - V - - - - - :
Given vectors A and V . . . B is the projection of A onto V.
. . . . . . . . . . . . . . . . .A·V
The formula is: .B . = . ----- V
. . . . . . . . . . . . . . . . .|V|²
. . . . . . . . . . . . . . .[2,-3,5]·[3,-2,5] . . . . . . .37
So we have: .B . = . --------------------- V . = . --- V
. . . . . . . . . . . . . . .(√3² + 2² + 5²)² . . . . . .38
Hence: .B .= .(37/38)[3,-2,5] .= .[111/38, -74/38, 185/38]
Another formula: . C .= .A - B
Hence: .C .= .[2, -3, 5] - [111/38, -74/38, 185/38] .= .[-35/38, -40/38, 5/38]
Therefore: .A .= .[111/38, -74/38, 185/38] + [-35/38, -40/38, 5/38]
Wow, thanks a LOT, that picture/diagram really makes it all clear! Great explaination btw as well. Once again, thank you, both of you! :)