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Consider a line which passes through the point P=(x1,y1,z1) P = ( x 1 , y 1 , z 1 ) and has direction vector d⃗ =(l,m,n), ...
... geometry (or Analytic geometry) in three-dimensional space, Points, lines and planes in three-dimensional coordinate system represented by vectors
Now, if we let n→=(a,b,c), n → = ( a , b , c ) , then since P0P−→− P 0 P → is perpendicular to n→, n → , we have
Vector addition for vectors at any angle | Adding vectors | How to add vectors
The three vectors spanning a parallelepiped have triple product equal to its volume.
Vector resolution equations used for vector addition of multiple vectors | More at plainphysics.com