Hello, Raman!

There are formulas for this problem . . .

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]